CINXE.COM

<!DOCTYPE html> <html lang="en"> <head> <meta content="text/html; charset=utf-8" http-equiv="content-type"/> <title>ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients</title>  <meta content="width=device-width, initial-scale=1, shrink-to-fit=no" name="viewport"/> <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.3.0/dist/css/bootstrap.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/ar5iv.0.7.9.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/ar5iv-fonts.0.7.9.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/latexml_styles.css" rel="stylesheet" type="text/css"/> <script src="https://cdn.jsdelivr.net/npm/bootstrap@5.3.0/dist/js/bootstrap.bundle.min.js"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/html2canvas/1.3.3/html2canvas.min.js"></script> <script src="/static/browse/0.3.4/js/addons_new.js"></script> <script src="/static/browse/0.3.4/js/feedbackOverlay.js"></script> <meta content="" lang="en" name="keywords"/> <base href="/html/2404.18165v1/"/></head> <body> <nav class="ltx_page_navbar"> <nav class="ltx_TOC"> <ol class="ltx_toclist"> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S1" title="In ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">1 Introduction</a></li> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S2" title="In ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">2 Data</a></li> <li class="ltx_tocentry ltx_tocentry_section"> <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3" title="In ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3 The ELEPHANT Pipeline</a> <ol class="ltx_toclist ltx_toclist_section"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.SS1" title="In 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3.1 Stamp pre-processing</a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.SS2" title="In 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3.2 Segmentation masks</a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.SS3" title="In 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3.3 Host categorization via Fourier power spectrum</a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_section"> <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4" title="In ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4 Results</a> <ol class="ltx_toclist ltx_toclist_section"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.SS1" title="In 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4.1 <math alttext="D" class="ltx_Math" display="inline"><semantics><mi>D</mi><annotation-xml encoding="MathML-Content"><ci>𝐷</ci></annotation-xml><annotation encoding="application/x-tex">D</annotation><annotation encoding="application/x-llamapun">italic_D</annotation></semantics></math> threshold for hostless candidates</a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.SS2" title="In 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4.2 Hostless sources on TNS</a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S5" title="In ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">5 Conclusions</a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#A1" title="In ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">A Nearest neighbor</a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#A2" title="In ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">B Segmentation masks with SExtractor</a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#A3" title="In ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">C Machine learning classified hostless candidates</a></li> </ol></nav> </nav> <div class="ltx_page_main"> <div class="ltx_page_content"> <article class="ltx_document ltx_authors_1line">11institutetext: The Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova 106 91, Stockholm, Sweden 22institutetext: Independent Researcher, Ingolstadt, Germany 33institutetext: Instituto de Astronomia, Geofísica e Ciências Atmosféricas da USP, 05508-900, São Paulo, Brazil 44institutetext: Institute of Astronomy and Kavli Institute for Cosmology, Madingley Road, Cambridge, CB3 0HA, UK 55institutetext: Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478 Warszawa, Poland 66institutetext: Université Clermont Auvergne, CNRS/IN2P3, LPC, F-63000 Clermont-Ferrand, France 77institutetext: CENTRA, Universidade de Lisboa, FCUL, Campo Grande, Edif. C8, 1749-016 Lisboa, Portugal 88institutetext: Donald Bren School of Information and Computer Sciences, University of California, Irvine, CA 92697, USA 99institutetext: Business School, University of Edinburgh, 29 Buccleuch Pl, Edinburgh, EH8 9JS, UK 1010institutetext: Centre for Statistics, University of Edinburgh, Peter Guthrie Tait Rd, Edinburgh, EH9 3FD, UK 1111institutetext: Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield, AL10 9AB, UK 1212institutetext: Independent Researcher, Budapest, Hungary 1313institutetext: School of Mathematical and Physical Sciences, Macquarie University, NSW 2109, Australia <h1 class="ltx_title ltx_title_document"> <img alt="[Uncaptioned image]" class="ltx_graphics ltx_img_square" height="17" id="id1.g1" src="x1.png" width="18"/> ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients </h1> <div class="ltx_authors"> P. J. Pessi 11 <a href="mailto:priscila.pessi@astro.su.se">priscila.pessi@astro.su.se</a> R. Durgesh 22 L. Nakazono 33 E. E. Hayes 44 R. A. P. Oliveira 55 E. E. O. Ishida 66 A. Moitinho 77 A. Krone-Martins 88 B. Moews 99 10 10 R. S. de Souza 1111 R. Beck 1212 M. A. Kuhn 1111 K. Nowak 1111 S. Vaughan (for the COIN collaboration) 1313 </div> <div class="ltx_abstract"> <h6 class="ltx_title ltx_title_abstract">Abstract</h6> Context. Transient astronomical events that exhibit no discernible association with a host galaxy are commonly referred to as hostless. These rare phenomena are associated with extremely energetic events, and they can offer unique insights into the properties and evolution of stars and galaxies. However, the sheer number of transients captured by contemporary high-cadence astronomical surveys renders the manual identification of all potential hostless transients impractical. Therefore, creating a systematic identification tool is crucial for studying these elusive events. Aims. We present the ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients (ELEPHANT), a framework for filtering hostless transients in astronomical data streams. It was designed to process alerts from the Zwicky Transient Facility (ZTF) as presented in the Fink broker; however, its underlying concept can be applied to other data sources. Methods. We used Fink to access all the ZTF alerts produced between January/2022 and December/2023, selecting alerts associated with extragalactic transients reported in SIMBAD or TNS, as well as those classified as supernova (SN) or kilonova (KN) by the machine learning (ML) classifiers within the broker. We then processed the associated stamps using a sequence of image analysis techniques to retrieve hostless candidates. Results. We find that <math alttext="\lesssim" class="ltx_Math" display="inline" id="id2.1.m1.1"><semantics id="id2.1.m1.1a"><mo id="id2.1.m1.1.1" xref="id2.1.m1.1.1.cmml">≲</mo><annotation-xml encoding="MathML-Content" id="id2.1.m1.1b"><csymbol cd="latexml" id="id2.1.m1.1.1.cmml" xref="id2.1.m1.1.1">less-than-or-similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="id2.1.m1.1c">\lesssim</annotation><annotation encoding="application/x-llamapun" id="id2.1.m1.1d">≲</annotation></semantics></math> 2% of all analyzed transients are potentially hostless. Among them, only <math alttext="\sim" class="ltx_Math" display="inline" id="id3.2.m2.1"><semantics id="id3.2.m2.1a"><mo id="id3.2.m2.1.1" xref="id3.2.m2.1.1.cmml">∼</mo><annotation-xml encoding="MathML-Content" id="id3.2.m2.1b"><csymbol cd="latexml" id="id3.2.m2.1.1.cmml" xref="id3.2.m2.1.1">similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="id3.2.m2.1c">\sim</annotation><annotation encoding="application/x-llamapun" id="id3.2.m2.1d">∼</annotation></semantics></math> 10% have a spectroscopic class reported on TNS, with Type Ia supernova being the most common class, followed by superluminous supernova. In particular, among the hostless candidates retrieved by our pipeline, there was SN 2018ibb, which has been proposed to be a Pair Instability SN candidate; and SN 2022ann, one of only five known SNe Icn. When no class is reported on TNS, the dominant classes are QSO and SN candidates, with the former obtained from SIMBAD and the latter inferred using the Fink ML classifier. Conclusions. ELEPHANT represents an effective strategy to filter extragalactic events within large and complex astronomical alert streams. There are many applications for which this pipeline will be useful, ranging from transient selection for follow-up to studies of transient environments. The results presented here demonstrate the feasibility of developing specially crafted pipelines that enable a variety of scientific studies based on large-scale surveys. ELEPHANT is publicly available in the COINToolbox: <a class="ltx_ref ltx_url ltx_font_typewriter" href="https://github.com/COINtoolbox/extragalactic_hostless" title="">https://github.com/COINtoolbox/extragalactic_hostless</a>. </div> <div class="ltx_keywords"> <h6 class="ltx_title ltx_title_keywords">Key Words.: </h6> Methods: data analysis – Astronomical databases: miscellaneous – Stars: general – Methods: statistical </div> <section class="ltx_section" id="S1"> <h2 class="ltx_title ltx_title_section"> 1 Introduction</h2> <div class="ltx_para" id="S1.p1"> Contemporary wide-field, untargeted surveys that scan large portions of the sky on a regular basis, such as the All-Sky Automated Survey for Supernovae <cite class="ltx_cite ltx_citemacro_citep">(ASAS-SN, Shappee et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib47" title="">2014</a>)</cite>, Gaia <cite class="ltx_cite ltx_citemacro_citep">(Gaia Collaboration et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib17" title="">2016</a>)</cite>, the Asteroid Terrestrial-impact Last Alert System <cite class="ltx_cite ltx_citemacro_citep">(ATLAS, Tonry et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib49" title="">2018</a>)</cite> and the Zwicky Transient Facility (ZTF; <cite class="ltx_cite ltx_citemacro_citet">Bellm et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib7" title="">2019</a></cite>), have significantly increased the number of transients discovered nightly over the past decades111See <cite class="ltx_cite ltx_citemacro_cite">Yamaoka (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib52" title="">2017</a>)</cite> for numbers on the growth of discovered and classified supernovae from 1991 to 2015. For statistics on transient discovery and classification from 2016 onward, refer to <a class="ltx_ref ltx_url ltx_font_typewriter" href="https://www.wis-tns.org/stats-maps" title="">https://www.wis-tns.org/stats-maps</a>.. Such projects have not only increased the number of confirmed transients of known classes but have also facilitated the discovery of new classes of events <cite class="ltx_cite ltx_citemacro_citep">(e.g., Drout et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib13" title="">2014</a>; Kankare et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib28" title="">2017</a>)</cite>. Thus, the past decade has witnessed a significant increase and diversification of the transient sky landscape, populated by a myriad of objects <cite class="ltx_cite ltx_citemacro_citep">(e.g. Hambleton et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib25" title="">2023</a>)</cite>. </div> <div class="ltx_para" id="S1.p2"> Extragalactic transients can be described as the observational consequence of energetic events taking place outside the Milky Way. This description implies a progenitor population of astrophysical sources which should, in principle, be associated to a host galaxy. Nevertheless, a small fraction of transients seem to not be associated to any host and are thus considered hostless <cite class="ltx_cite ltx_citemacro_citep">(e.g. Qin et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib43" title="">2022</a>, <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib42" title="">2024</a>)</cite>. In these cases, the host may remain undetected either because it is fainter than the survey’s limiting magnitude or because the transient was produced by a progenitor that achieved hypervelocity and escaped its host galaxy <cite class="ltx_cite ltx_citemacro_citep">(e.g., Martin <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib35" title="">2006</a>; Zinn et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib53" title="">2011</a>)</cite>. Hostless transients have been associated with superluminous supernovae <cite class="ltx_cite ltx_citemacro_citep">(SLSNe; e.g. McCrum et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib38" title="">2015</a>)</cite>, gamma-ray burst <cite class="ltx_cite ltx_citemacro_citep">(GRBs; e.g. Ho et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib26" title="">2020</a>)</cite>, Fast X-ray transients <cite class="ltx_cite ltx_citemacro_citep">(FXTs; e.g. Gillanders et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib20" title="">2024</a>)</cite> and lensed transients <cite class="ltx_cite ltx_citemacro_citep">(e.g. Ryczanowski et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib45" title="">2020</a>)</cite>, among others. Independently of the exact mechanism that rendered them hostless, such rare events represent an opportunity to further investigate peculiar astrophysical scenarios and may provide important clues regarding their local environment. They have already been used to discover low surface brightness galaxies <cite class="ltx_cite ltx_citemacro_citep">(LSB, Zinn et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib54" title="">2012</a>)</cite> and to study intra-cluster stellar populations <cite class="ltx_cite ltx_citemacro_citep">(Graham et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib24" title="">2015</a>)</cite>. </div> <div class="ltx_para" id="S1.p3"> Given such scientific potential, whenever a hostless transient is discovered, it sparks the interest of the astronomical community focused on rare events. In the past, the moderate number of discovered transients allowed thorough investigation of each candidate together with their associated hosts <cite class="ltx_cite ltx_citemacro_citep">(e.g., Filippenko <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib15" title="">1997</a>; Baldwin et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib5" title="">1981</a>)</cite>. Nowadays, untargeted searches are discovering transients in fainter and more distant host galaxies, substantially increasing their numbers and rendering it impossible to study all of them in detail. As an example, ZTF currently detects a few hundred thousand transient candidates per night, while the upcoming Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to detect around 10 million per night over a period of 10 years <cite class="ltx_cite ltx_citemacro_citep">(Bellm et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib6" title="">2019</a>)</cite>. In this context, it became necessary to develop automated frameworks for mining large astronomical datasets. </div> <div class="ltx_para" id="S1.p4"> In this work, we introduce the ExtragaLactic alErt Pipeline for Hostless Transients (ELEPHANT), whose goal is to enable automatic identification of confirmed or potential extragalactic events without an obvious host association. It significantly reduces the number of candidates requiring visual inspection, thus allowing an optimal allocation of expert time and follow-up resources. ELEPHANT employs a range of established image processing techniques to analyze image stamps associated with each transient, assessing the likelihood of a host’s presence. We detail the components of our pipeline and discuss a number of noteworthy candidates identified during its development. We visually inspected candidates with an associated spectroscopic classification available on the Transient Name Server (TNS222<a class="ltx_ref ltx_url ltx_font_typewriter" href="https://www.wis-tns.org/" title="">https://www.wis-tns.org/</a>) to confirm their hostless nature. This process also helped us define statistical thresholds to apply to the rest of the sample. We found that less than <math alttext="\lesssim" class="ltx_Math" display="inline" id="S1.p4.1.m1.1"><semantics id="S1.p4.1.m1.1a"><mo id="S1.p4.1.m1.1.1" xref="S1.p4.1.m1.1.1.cmml">≲</mo><annotation-xml encoding="MathML-Content" id="S1.p4.1.m1.1b"><csymbol cd="latexml" id="S1.p4.1.m1.1.1.cmml" xref="S1.p4.1.m1.1.1">less-than-or-similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S1.p4.1.m1.1c">\lesssim</annotation><annotation encoding="application/x-llamapun" id="S1.p4.1.m1.1d">≲</annotation></semantics></math> 2% of the analyzed sample is potentially hostless, with the most common classes of hostless candidates being QSOs, Type Ia SN, and SLSN. Some hostless candidates identified by our pipeline, which present interesting features, had already been thoroughly discussed in the literature (see Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4" title="4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4</a>). Our results illustrate the potential of the pipeline if applied to more recent data. We are currently working in integrating it to the Fink broker <cite class="ltx_cite ltx_citemacro_citep">(Möller et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib40" title="">2021</a>)</cite>, which will allow processing ZTF alert stream in real time and increase the chances of identifying hostless transients while they are still bright enough for spectroscopic follow-up. </div> <div class="ltx_para" id="S1.p5"> This paper is organized as follows: Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S2" title="2 Data ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">2</a> outlines the data selected for this analysis. Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3" title="3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3</a> describes the ELEPHANT workflow. Results are presented in Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4" title="4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4</a> and conclusions in Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S5" title="5 Conclusions ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">5</a>. </div> </section> <section class="ltx_section" id="S2"> <h2 class="ltx_title ltx_title_section"> 2 Data</h2> <div class="ltx_para" id="S2.p1"> We use image data available within alerts distributed by ZTF. An alert package is produced when the difference imaging pipeline identifies a transient source. It includes photometric history, metadata, and three stamps: the original reference image – template, the new observation – science, and the difference image – difference <cite class="ltx_cite ltx_citemacro_citep">(Bellm et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib7" title="">2019</a>; Masci et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib36" title="">2019</a>)</cite>. This information is distributed nightly to community brokers, whose task is to filter, add value, and redistribute the alerts to domain experts. This work uses the alert stream information as provided by the Fink broker <cite class="ltx_cite ltx_citemacro_citep">(Möller et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib40" title="">2021</a>)</cite>, however the pipeline is flexible enough to be used with other data sources333Other known community brokers include ALERCE <cite class="ltx_cite ltx_citemacro_citep">(Förster et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib16" title="">2021</a>)</cite>, AMPEL <cite class="ltx_cite ltx_citemacro_citep">(Nordin et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib41" title="">2019</a>)</cite>, ANTARES <cite class="ltx_cite ltx_citemacro_citep">(Matheson et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib37" title="">2021</a>)</cite>, Babamul, LASAIR <cite class="ltx_cite ltx_citemacro_citep">(Williams et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib51" title="">2024</a>)</cite> and Pitt-Google.. </div> <div class="ltx_para" id="S2.p2"> We retrieved all alerts processed by Fink between January/2022 and December/2023. The data set contained 70 176 557 alerts, which correspond to 17 683 691 objects. Approximately 50% of these have an associated classification. We only keep events associated with an extragalactic transient classification, including all classes of active galactic nuclei (AGN), supernovae (SNe), and kilonova candidates, among others (the complete list of the classes considered for this work can be found in our repository444<a class="ltx_ref ltx_url ltx_font_typewriter" href="https://github.com/COINtoolbox/extragalactic_hostless" title="">https://github.com/COINtoolbox/extragalactic_hostless</a>). The classifications provided by Fink are obtained via cross-match with SIMBAD555<a class="ltx_ref ltx_url ltx_font_typewriter" href="https://simbad.cds.unistra.fr/simbad/" title="">https://simbad.cds.unistra.fr/simbad/</a> <cite class="ltx_cite ltx_citemacro_citep">(Wenger et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib50" title="">2000</a>)</cite>, the Transient Name Server666<a class="ltx_ref ltx_url ltx_font_typewriter" href="https://www.wis-tns.org/" title="">https://www.wis-tns.org/</a> (TNS), or produced by machine learning (ML) algorithms used by the broker <cite class="ltx_cite ltx_citemacro_citep">(Möller & de Boissière <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib39" title="">2020</a>; Leoni et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib31" title="">2022</a>; Biswas et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib9" title="">2023</a>)</cite>. In case a cataloged classification is available, we consider it to be final. However, ML-based classifications are given per alert. Since one object can produce many alerts, this sometimes results in different classes associated with the same astrophysical source. When selecting sources for which only ML classification is available, the final class was chosen by majority vote, taking into account all alerts associated with the same object. </div> <div class="ltx_para" id="S2.p3"> We exclude alerts with no associated classification or associated with galactic transients such as variable stars or objects present in the Minor Planet Center777<a class="ltx_ref ltx_url ltx_font_typewriter" href="https://minorplanetcenter.net/about" title="">https://minorplanetcenter.net/about</a>. Since we are only interested in hostless events, we also considered cross-match with the MANGROVE catalog <cite class="ltx_cite ltx_citemacro_citep">(Ducoin et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib14" title="">2020</a>)</cite> and removed any object associated with a known host, even if the host galaxy association is tentative. We keep only <math alttext="\sim" class="ltx_Math" display="inline" id="S2.p3.1.m1.1"><semantics id="S2.p3.1.m1.1a"><mo id="S2.p3.1.m1.1.1" xref="S2.p3.1.m1.1.1.cmml">∼</mo><annotation-xml encoding="MathML-Content" id="S2.p3.1.m1.1b"><csymbol cd="latexml" id="S2.p3.1.m1.1.1.cmml" xref="S2.p3.1.m1.1.1">similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S2.p3.1.m1.1c">\sim</annotation><annotation encoding="application/x-llamapun" id="S2.p3.1.m1.1d">∼</annotation></semantics></math> 3.5% of the original alerts by applying these conditions. To eliminate potentially bogus events, we only consider transients with two or more alerts, meaning that they will have more than one associated set of stamps. The stamps are typically <math alttext="63\times 63" class="ltx_Math" display="inline" id="S2.p3.2.m2.1"><semantics id="S2.p3.2.m2.1a"><mrow id="S2.p3.2.m2.1.1" xref="S2.p3.2.m2.1.1.cmml"><mn id="S2.p3.2.m2.1.1.2" xref="S2.p3.2.m2.1.1.2.cmml">63</mn><mo id="S2.p3.2.m2.1.1.1" lspace="0.222em" rspace="0.222em" xref="S2.p3.2.m2.1.1.1.cmml">×</mo><mn id="S2.p3.2.m2.1.1.3" xref="S2.p3.2.m2.1.1.3.cmml">63</mn></mrow><annotation-xml encoding="MathML-Content" id="S2.p3.2.m2.1b"><apply id="S2.p3.2.m2.1.1.cmml" xref="S2.p3.2.m2.1.1"><times id="S2.p3.2.m2.1.1.1.cmml" xref="S2.p3.2.m2.1.1.1"></times><cn id="S2.p3.2.m2.1.1.2.cmml" type="integer" xref="S2.p3.2.m2.1.1.2">63</cn><cn id="S2.p3.2.m2.1.1.3.cmml" type="integer" xref="S2.p3.2.m2.1.1.3">63</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p3.2.m2.1c">63\times 63</annotation><annotation encoding="application/x-llamapun" id="S2.p3.2.m2.1d">63 × 63</annotation></semantics></math> pixels with the detected transient located at the center. Smaller alerts are produced in rare cases, normally related to detector edge effects or due to defects in the image acquisition process <cite class="ltx_cite ltx_citemacro_citep">(Reyes-Jainaga et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib44" title="">2023</a>)</cite>. To guarantee a homogeneous sample, we removed any stamp whose size is smaller than the typical value. After applying these last conditions, we end with a total of 90 928 transients. </div> <figure class="ltx_figure" id="S2.F1"><img alt="Refer to caption" class="ltx_graphics ltx_img_square" height="830" id="S2.F1.g1" src="x2.png" width="830"/> <figcaption class="ltx_caption">Figure 1: Example of the template (left) and science (right) stamps for a transient associated with a host galaxy. The top row shows the original stamps and the bottom row shows the masks produced from sigma clipping. At the center of the stamps, we display a red circle of 7 pix radius that indicates the aperture radius of the associated photometry.</figcaption> </figure> </section> <section class="ltx_section" id="S3"> <h2 class="ltx_title ltx_title_section"> 3 The ELEPHANT Pipeline</h2> <div class="ltx_para" id="S3.p1"> The pipeline analyses both the science and template stamps in parallel. Thus, a source is considered hostless if either its template or science stamps survives all filtering stages. In principle, the template image should suffice to detect the presence of a possible host, however, because of the template generation process <cite class="ltx_cite ltx_citemacro_citep">(see Masci et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib36" title="">2019</a>)</cite>, some of them can suffer from transient contamination. In these cases, the transient would be detected as a source in the center of the template image, leading to the wrong detection of a host. Considering both the template and science stamps attenuates this issue. Below, we describe each step of the pipeline. </div> <section class="ltx_subsection" id="S3.SS1"> <h3 class="ltx_title ltx_title_subsection"> 3.1 Stamp pre-processing</h3> <div class="ltx_para" id="S3.SS1.p1"> If a stamp contains pixels with missing or empty values, the pipeline estimates the probability density function (PDF) of the counts in the remaining pixels via Gaussian resampling using the scipy.stats.gaussian_kde Python method. The empty value is then replaced by randomly selected values from the resulting PDF, producing a homogenized sample where all images have the same number of valid pixels. Additionally, we use the full-width at half maximum (FWHM) of each stamp to estimate the image quality. In our sample, the FWHM can vary from <math alttext="\rm{FWHM}<1.0^{\prime\prime}" class="ltx_Math" display="inline" id="S3.SS1.p1.1.m1.1"><semantics id="S3.SS1.p1.1.m1.1a"><mrow id="S3.SS1.p1.1.m1.1.1" xref="S3.SS1.p1.1.m1.1.1.cmml"><mi id="S3.SS1.p1.1.m1.1.1.2" xref="S3.SS1.p1.1.m1.1.1.2.cmml">FWHM</mi><mo id="S3.SS1.p1.1.m1.1.1.1" xref="S3.SS1.p1.1.m1.1.1.1.cmml"><</mo><msup id="S3.SS1.p1.1.m1.1.1.3" xref="S3.SS1.p1.1.m1.1.1.3.cmml"><mn id="S3.SS1.p1.1.m1.1.1.3.2" xref="S3.SS1.p1.1.m1.1.1.3.2.cmml">1.0</mn><mo id="S3.SS1.p1.1.m1.1.1.3.3" xref="S3.SS1.p1.1.m1.1.1.3.3.cmml">′′</mo></msup></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p1.1.m1.1b"><apply id="S3.SS1.p1.1.m1.1.1.cmml" xref="S3.SS1.p1.1.m1.1.1"><lt id="S3.SS1.p1.1.m1.1.1.1.cmml" xref="S3.SS1.p1.1.m1.1.1.1"></lt><ci id="S3.SS1.p1.1.m1.1.1.2.cmml" xref="S3.SS1.p1.1.m1.1.1.2">FWHM</ci><apply id="S3.SS1.p1.1.m1.1.1.3.cmml" xref="S3.SS1.p1.1.m1.1.1.3"><csymbol cd="ambiguous" id="S3.SS1.p1.1.m1.1.1.3.1.cmml" xref="S3.SS1.p1.1.m1.1.1.3">superscript</csymbol><cn id="S3.SS1.p1.1.m1.1.1.3.2.cmml" type="float" xref="S3.SS1.p1.1.m1.1.1.3.2">1.0</cn><ci id="S3.SS1.p1.1.m1.1.1.3.3.cmml" xref="S3.SS1.p1.1.m1.1.1.3.3">′′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p1.1.m1.1c">\rm{FWHM}<1.0^{\prime\prime}</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p1.1.m1.1d">roman_FWHM < 1.0 start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT</annotation></semantics></math> (a few cases) to <math alttext="\rm{FWHM}>3.0^{\prime\prime}" class="ltx_Math" display="inline" id="S3.SS1.p1.2.m2.1"><semantics id="S3.SS1.p1.2.m2.1a"><mrow id="S3.SS1.p1.2.m2.1.1" xref="S3.SS1.p1.2.m2.1.1.cmml"><mi id="S3.SS1.p1.2.m2.1.1.2" xref="S3.SS1.p1.2.m2.1.1.2.cmml">FWHM</mi><mo id="S3.SS1.p1.2.m2.1.1.1" xref="S3.SS1.p1.2.m2.1.1.1.cmml">></mo><msup id="S3.SS1.p1.2.m2.1.1.3" xref="S3.SS1.p1.2.m2.1.1.3.cmml"><mn id="S3.SS1.p1.2.m2.1.1.3.2" xref="S3.SS1.p1.2.m2.1.1.3.2.cmml">3.0</mn><mo id="S3.SS1.p1.2.m2.1.1.3.3" xref="S3.SS1.p1.2.m2.1.1.3.3.cmml">′′</mo></msup></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p1.2.m2.1b"><apply id="S3.SS1.p1.2.m2.1.1.cmml" xref="S3.SS1.p1.2.m2.1.1"><gt id="S3.SS1.p1.2.m2.1.1.1.cmml" xref="S3.SS1.p1.2.m2.1.1.1"></gt><ci id="S3.SS1.p1.2.m2.1.1.2.cmml" xref="S3.SS1.p1.2.m2.1.1.2">FWHM</ci><apply id="S3.SS1.p1.2.m2.1.1.3.cmml" xref="S3.SS1.p1.2.m2.1.1.3"><csymbol cd="ambiguous" id="S3.SS1.p1.2.m2.1.1.3.1.cmml" xref="S3.SS1.p1.2.m2.1.1.3">superscript</csymbol><cn id="S3.SS1.p1.2.m2.1.1.3.2.cmml" type="float" xref="S3.SS1.p1.2.m2.1.1.3.2">3.0</cn><ci id="S3.SS1.p1.2.m2.1.1.3.3.cmml" xref="S3.SS1.p1.2.m2.1.1.3.3">′′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p1.2.m2.1c">\rm{FWHM}>3.0^{\prime\prime}</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p1.2.m2.1d">roman_FWHM > 3.0 start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT</annotation></semantics></math>, with a median value of <math alttext="\rm{FWHM}\sim 2.0^{\prime\prime}" class="ltx_Math" display="inline" id="S3.SS1.p1.3.m3.1"><semantics id="S3.SS1.p1.3.m3.1a"><mrow id="S3.SS1.p1.3.m3.1.1" xref="S3.SS1.p1.3.m3.1.1.cmml"><mi id="S3.SS1.p1.3.m3.1.1.2" xref="S3.SS1.p1.3.m3.1.1.2.cmml">FWHM</mi><mo id="S3.SS1.p1.3.m3.1.1.1" xref="S3.SS1.p1.3.m3.1.1.1.cmml">∼</mo><msup id="S3.SS1.p1.3.m3.1.1.3" xref="S3.SS1.p1.3.m3.1.1.3.cmml"><mn id="S3.SS1.p1.3.m3.1.1.3.2" xref="S3.SS1.p1.3.m3.1.1.3.2.cmml">2.0</mn><mo id="S3.SS1.p1.3.m3.1.1.3.3" xref="S3.SS1.p1.3.m3.1.1.3.3.cmml">′′</mo></msup></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p1.3.m3.1b"><apply id="S3.SS1.p1.3.m3.1.1.cmml" xref="S3.SS1.p1.3.m3.1.1"><csymbol cd="latexml" id="S3.SS1.p1.3.m3.1.1.1.cmml" xref="S3.SS1.p1.3.m3.1.1.1">similar-to</csymbol><ci id="S3.SS1.p1.3.m3.1.1.2.cmml" xref="S3.SS1.p1.3.m3.1.1.2">FWHM</ci><apply id="S3.SS1.p1.3.m3.1.1.3.cmml" xref="S3.SS1.p1.3.m3.1.1.3"><csymbol cd="ambiguous" id="S3.SS1.p1.3.m3.1.1.3.1.cmml" xref="S3.SS1.p1.3.m3.1.1.3">superscript</csymbol><cn id="S3.SS1.p1.3.m3.1.1.3.2.cmml" type="float" xref="S3.SS1.p1.3.m3.1.1.3.2">2.0</cn><ci id="S3.SS1.p1.3.m3.1.1.3.3.cmml" xref="S3.SS1.p1.3.m3.1.1.3.3">′′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p1.3.m3.1c">\rm{FWHM}\sim 2.0^{\prime\prime}</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p1.3.m3.1d">roman_FWHM ∼ 2.0 start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT</annotation></semantics></math>. To select only the best available images representing each astrophysical source, all alerts associated with a given source are separated into 3 FWHM bins: <math alttext="\rm{FWHM}<1.0^{\prime\prime}" class="ltx_Math" display="inline" id="S3.SS1.p1.4.m4.1"><semantics id="S3.SS1.p1.4.m4.1a"><mrow id="S3.SS1.p1.4.m4.1.1" xref="S3.SS1.p1.4.m4.1.1.cmml"><mi id="S3.SS1.p1.4.m4.1.1.2" xref="S3.SS1.p1.4.m4.1.1.2.cmml">FWHM</mi><mo id="S3.SS1.p1.4.m4.1.1.1" xref="S3.SS1.p1.4.m4.1.1.1.cmml"><</mo><msup id="S3.SS1.p1.4.m4.1.1.3" xref="S3.SS1.p1.4.m4.1.1.3.cmml"><mn id="S3.SS1.p1.4.m4.1.1.3.2" xref="S3.SS1.p1.4.m4.1.1.3.2.cmml">1.0</mn><mo id="S3.SS1.p1.4.m4.1.1.3.3" xref="S3.SS1.p1.4.m4.1.1.3.3.cmml">′′</mo></msup></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p1.4.m4.1b"><apply id="S3.SS1.p1.4.m4.1.1.cmml" xref="S3.SS1.p1.4.m4.1.1"><lt id="S3.SS1.p1.4.m4.1.1.1.cmml" xref="S3.SS1.p1.4.m4.1.1.1"></lt><ci id="S3.SS1.p1.4.m4.1.1.2.cmml" xref="S3.SS1.p1.4.m4.1.1.2">FWHM</ci><apply id="S3.SS1.p1.4.m4.1.1.3.cmml" xref="S3.SS1.p1.4.m4.1.1.3"><csymbol cd="ambiguous" id="S3.SS1.p1.4.m4.1.1.3.1.cmml" xref="S3.SS1.p1.4.m4.1.1.3">superscript</csymbol><cn id="S3.SS1.p1.4.m4.1.1.3.2.cmml" type="float" xref="S3.SS1.p1.4.m4.1.1.3.2">1.0</cn><ci id="S3.SS1.p1.4.m4.1.1.3.3.cmml" xref="S3.SS1.p1.4.m4.1.1.3.3">′′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p1.4.m4.1c">\rm{FWHM}<1.0^{\prime\prime}</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p1.4.m4.1d">roman_FWHM < 1.0 start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT</annotation></semantics></math>, <math alttext="1.0^{\prime\prime}<\rm{FWHM}<2.0^{\prime\prime}" class="ltx_Math" display="inline" id="S3.SS1.p1.5.m5.1"><semantics id="S3.SS1.p1.5.m5.1a"><mrow id="S3.SS1.p1.5.m5.1.1" xref="S3.SS1.p1.5.m5.1.1.cmml"><msup id="S3.SS1.p1.5.m5.1.1.2" xref="S3.SS1.p1.5.m5.1.1.2.cmml"><mn id="S3.SS1.p1.5.m5.1.1.2.2" xref="S3.SS1.p1.5.m5.1.1.2.2.cmml">1.0</mn><mo id="S3.SS1.p1.5.m5.1.1.2.3" xref="S3.SS1.p1.5.m5.1.1.2.3.cmml">′′</mo></msup><mo id="S3.SS1.p1.5.m5.1.1.3" xref="S3.SS1.p1.5.m5.1.1.3.cmml"><</mo><mi id="S3.SS1.p1.5.m5.1.1.4" xref="S3.SS1.p1.5.m5.1.1.4.cmml">FWHM</mi><mo id="S3.SS1.p1.5.m5.1.1.5" xref="S3.SS1.p1.5.m5.1.1.5.cmml"><</mo><msup id="S3.SS1.p1.5.m5.1.1.6" xref="S3.SS1.p1.5.m5.1.1.6.cmml"><mn id="S3.SS1.p1.5.m5.1.1.6.2" xref="S3.SS1.p1.5.m5.1.1.6.2.cmml">2.0</mn><mo id="S3.SS1.p1.5.m5.1.1.6.3" xref="S3.SS1.p1.5.m5.1.1.6.3.cmml">′′</mo></msup></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p1.5.m5.1b"><apply id="S3.SS1.p1.5.m5.1.1.cmml" xref="S3.SS1.p1.5.m5.1.1"><and id="S3.SS1.p1.5.m5.1.1a.cmml" xref="S3.SS1.p1.5.m5.1.1"></and><apply id="S3.SS1.p1.5.m5.1.1b.cmml" xref="S3.SS1.p1.5.m5.1.1"><lt id="S3.SS1.p1.5.m5.1.1.3.cmml" xref="S3.SS1.p1.5.m5.1.1.3"></lt><apply id="S3.SS1.p1.5.m5.1.1.2.cmml" xref="S3.SS1.p1.5.m5.1.1.2"><csymbol cd="ambiguous" id="S3.SS1.p1.5.m5.1.1.2.1.cmml" xref="S3.SS1.p1.5.m5.1.1.2">superscript</csymbol><cn id="S3.SS1.p1.5.m5.1.1.2.2.cmml" type="float" xref="S3.SS1.p1.5.m5.1.1.2.2">1.0</cn><ci id="S3.SS1.p1.5.m5.1.1.2.3.cmml" xref="S3.SS1.p1.5.m5.1.1.2.3">′′</ci></apply><ci id="S3.SS1.p1.5.m5.1.1.4.cmml" xref="S3.SS1.p1.5.m5.1.1.4">FWHM</ci></apply><apply id="S3.SS1.p1.5.m5.1.1c.cmml" xref="S3.SS1.p1.5.m5.1.1"><lt id="S3.SS1.p1.5.m5.1.1.5.cmml" xref="S3.SS1.p1.5.m5.1.1.5"></lt><share href="https://arxiv.org/html/2404.18165v1#S3.SS1.p1.5.m5.1.1.4.cmml" id="S3.SS1.p1.5.m5.1.1d.cmml" xref="S3.SS1.p1.5.m5.1.1"></share><apply id="S3.SS1.p1.5.m5.1.1.6.cmml" xref="S3.SS1.p1.5.m5.1.1.6"><csymbol cd="ambiguous" id="S3.SS1.p1.5.m5.1.1.6.1.cmml" xref="S3.SS1.p1.5.m5.1.1.6">superscript</csymbol><cn id="S3.SS1.p1.5.m5.1.1.6.2.cmml" type="float" xref="S3.SS1.p1.5.m5.1.1.6.2">2.0</cn><ci id="S3.SS1.p1.5.m5.1.1.6.3.cmml" xref="S3.SS1.p1.5.m5.1.1.6.3">′′</ci></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p1.5.m5.1c">1.0^{\prime\prime}<\rm{FWHM}<2.0^{\prime\prime}</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p1.5.m5.1d">1.0 start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT < roman_FWHM < 2.0 start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT</annotation></semantics></math> and <math alttext="\rm{FWHM}>2.0^{\prime\prime}" class="ltx_Math" display="inline" id="S3.SS1.p1.6.m6.1"><semantics id="S3.SS1.p1.6.m6.1a"><mrow id="S3.SS1.p1.6.m6.1.1" xref="S3.SS1.p1.6.m6.1.1.cmml"><mi id="S3.SS1.p1.6.m6.1.1.2" xref="S3.SS1.p1.6.m6.1.1.2.cmml">FWHM</mi><mo id="S3.SS1.p1.6.m6.1.1.1" xref="S3.SS1.p1.6.m6.1.1.1.cmml">></mo><msup id="S3.SS1.p1.6.m6.1.1.3" xref="S3.SS1.p1.6.m6.1.1.3.cmml"><mn id="S3.SS1.p1.6.m6.1.1.3.2" xref="S3.SS1.p1.6.m6.1.1.3.2.cmml">2.0</mn><mo id="S3.SS1.p1.6.m6.1.1.3.3" xref="S3.SS1.p1.6.m6.1.1.3.3.cmml">′′</mo></msup></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p1.6.m6.1b"><apply id="S3.SS1.p1.6.m6.1.1.cmml" xref="S3.SS1.p1.6.m6.1.1"><gt id="S3.SS1.p1.6.m6.1.1.1.cmml" xref="S3.SS1.p1.6.m6.1.1.1"></gt><ci id="S3.SS1.p1.6.m6.1.1.2.cmml" xref="S3.SS1.p1.6.m6.1.1.2">FWHM</ci><apply id="S3.SS1.p1.6.m6.1.1.3.cmml" xref="S3.SS1.p1.6.m6.1.1.3"><csymbol cd="ambiguous" id="S3.SS1.p1.6.m6.1.1.3.1.cmml" xref="S3.SS1.p1.6.m6.1.1.3">superscript</csymbol><cn id="S3.SS1.p1.6.m6.1.1.3.2.cmml" type="float" xref="S3.SS1.p1.6.m6.1.1.3.2">2.0</cn><ci id="S3.SS1.p1.6.m6.1.1.3.3.cmml" xref="S3.SS1.p1.6.m6.1.1.3.3">′′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p1.6.m6.1c">\rm{FWHM}>2.0^{\prime\prime}</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p1.6.m6.1d">roman_FWHM > 2.0 start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT</annotation></semantics></math>. The pipeline only considers the stamps in the smallest available FWHM bin for each source, discarding all others. </div> <div class="ltx_para" id="S3.SS1.p2"> All selected stamps for a given object are then stacked by adopting the median count value in each pixel of the <math alttext="63\times 63" class="ltx_Math" display="inline" id="S3.SS1.p2.1.m1.1"><semantics id="S3.SS1.p2.1.m1.1a"><mrow id="S3.SS1.p2.1.m1.1.1" xref="S3.SS1.p2.1.m1.1.1.cmml"><mn id="S3.SS1.p2.1.m1.1.1.2" xref="S3.SS1.p2.1.m1.1.1.2.cmml">63</mn><mo id="S3.SS1.p2.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="S3.SS1.p2.1.m1.1.1.1.cmml">×</mo><mn id="S3.SS1.p2.1.m1.1.1.3" xref="S3.SS1.p2.1.m1.1.1.3.cmml">63</mn></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p2.1.m1.1b"><apply id="S3.SS1.p2.1.m1.1.1.cmml" xref="S3.SS1.p2.1.m1.1.1"><times id="S3.SS1.p2.1.m1.1.1.1.cmml" xref="S3.SS1.p2.1.m1.1.1.1"></times><cn id="S3.SS1.p2.1.m1.1.1.2.cmml" type="integer" xref="S3.SS1.p2.1.m1.1.1.2">63</cn><cn id="S3.SS1.p2.1.m1.1.1.3.cmml" type="integer" xref="S3.SS1.p2.1.m1.1.1.3">63</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p2.1.m1.1c">63\times 63</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p2.1.m1.1d">63 × 63</annotation></semantics></math> cutout. This stacking process aids to enhance the images’ signal-to-noise ratio (S/N), thereby improving the identification of potential hosts. Since the science stamps result from a single exposure, this process impacts them much more than their template counterparts. Nevertheless, this technique also serves to homogenize the effects of varying templates used throughout the lifespan of a given transient. </div> </section> <section class="ltx_subsection" id="S3.SS2"> <h3 class="ltx_title ltx_title_subsection"> 3.2 Segmentation masks</h3> <figure class="ltx_figure" id="S3.F2"><img alt="Refer to caption" class="ltx_graphics ltx_img_square" height="830" id="S3.F2.g1" src="x3.png" width="830"/> <figcaption class="ltx_caption">Figure 2: Example of the template (left) and science (right) stamps of a hostless transient candidate. The top row shows the original stamps, and the bottom row shows the masks produced by sigma clipping. We can see that the science stamp shows a mask at the center of the stamp that is absent in the template stamp. The absence of a mask is considered as the absence of a host. At the center of the stamps, we display a red circle of 7 pix radius that indicates the aperture radius of the associated photometry.</figcaption> </figure> <div class="ltx_para" id="S3.SS2.p1"> ELEPHANT uses sigma clipping to mask sources present in the stamps and uses those masks to detect the presence of a host galaxy. Sigma clipping is a typical method to detect outliers in astronomical images, usually used to remove the effect of defective pixels or cosmic rays by clipping out pixels above a given sigma threshold. The values of the clipped pixels can then be replaced with a mask or filled in with some characterization of the remaining image counts. </div> <div class="ltx_para" id="S3.SS2.p2"> The ZTF alert package includes the aperture magnitude of the transient obtained from aperture photometry, calculated considering a 7-pixel radius aperture. We use this size as a reference for the maximum size of any detected transient. ELEPHANT implements the astropy.stats.sigma_clip888<a class="ltx_ref ltx_url" href="https://docs.astropy.org/en/stable/api/astropy.stats.sigma_clip.html" title="">https://docs.astropy.org/en/stable/api/astropy.stats.sigma_clip.html</a> Python method considering <math alttext="\sigma=3" class="ltx_Math" display="inline" id="S3.SS2.p2.1.m1.1"><semantics id="S3.SS2.p2.1.m1.1a"><mrow id="S3.SS2.p2.1.m1.1.1" xref="S3.SS2.p2.1.m1.1.1.cmml"><mi id="S3.SS2.p2.1.m1.1.1.2" xref="S3.SS2.p2.1.m1.1.1.2.cmml">σ</mi><mo id="S3.SS2.p2.1.m1.1.1.1" xref="S3.SS2.p2.1.m1.1.1.1.cmml">=</mo><mn id="S3.SS2.p2.1.m1.1.1.3" xref="S3.SS2.p2.1.m1.1.1.3.cmml">3</mn></mrow><annotation-xml encoding="MathML-Content" id="S3.SS2.p2.1.m1.1b"><apply id="S3.SS2.p2.1.m1.1.1.cmml" xref="S3.SS2.p2.1.m1.1.1"><eq id="S3.SS2.p2.1.m1.1.1.1.cmml" xref="S3.SS2.p2.1.m1.1.1.1"></eq><ci id="S3.SS2.p2.1.m1.1.1.2.cmml" xref="S3.SS2.p2.1.m1.1.1.2">𝜎</ci><cn id="S3.SS2.p2.1.m1.1.1.3.cmml" type="integer" xref="S3.SS2.p2.1.m1.1.1.3">3</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p2.1.m1.1c">\sigma=3</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p2.1.m1.1d">italic_σ = 3</annotation></semantics></math>, median as the statistic to compute the clipping center value, and a maximum of ten iterations. As a result, any pixels above the selected median threshold are clipped. The clipped segments of the stamp are considered as the mask. If a mask bigger than 5 continuous pixels is found at the center of the science stamp but not at the center of the corresponding template stamp, or vice-versa, we flag the transient as a potential hostless candidate. </div> <div class="ltx_para" id="S3.SS2.p3"> ELEPHANT utilizes the obtained masks to identify the position of the pixel closest to the center that corresponds to a detected neighboring mask, considering any masked pixel within a 7-pixel square as indicative of a neighbor’s presence. Details on how the distance is computed can be found in Appendix <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#A1" title="Appendix A Nearest neighbor ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">A</a>. Although we don’t further use the distance information here, a future user could consider it to additionally assess the presence of a host. This could be useful when analyzing SN, as they could occur on the outskirts of their hosts. In such a case, a mask will not be found at the center of the stamp but close to it. In this context, what is considered to be close should be defined by the user. Another popular image segmentation software in astronomy is SExtractor; we decided not to use it here as it requires more resources than sigma clipping, and it also requires the pipeline to use out-of-memory processing; for further discussion on the use of SExtractor see Appendix <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#A2" title="Appendix B Segmentation masks with SExtractor ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">B</a>. </div> <div class="ltx_para" id="S3.SS2.p4"> After applying sigma clipping, ELEPHANT retrieves 1669 hostless candidates. Fig. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S2.F1" title="Figure 1 ‣ 2 Data ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">1</a> and Fig. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.F2" title="Figure 2 ‣ 3.2 Segmentation masks ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">2</a> show an example of a host detection and of the detection of a hostless candidate, respectively. Fig. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S2.F1" title="Figure 1 ‣ 2 Data ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">1</a> shows that the presence of a host galaxy at the center of the stamp is seen as a mask in the center of both the template and science stamps. On the other hand, Fig. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.F2" title="Figure 2 ‣ 3.2 Segmentation masks ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">2</a> shows that a mask is present at the center of only one of the transient’s stamps thus, it is flagged as a hostless candidate. Fig. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.F3" title="Figure 3 ‣ 3.2 Segmentation masks ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3</a> shows a spurious detection of a hostless candidate. In this case, the erroneous detection is driven by artifacts present on the template stamp. </div> <figure class="ltx_figure" id="S3.F3"><img alt="Refer to caption" class="ltx_graphics ltx_img_square" height="830" id="S3.F3.g1" src="x4.png" width="830"/> <figcaption class="ltx_caption">Figure 3: Example of the template (left) and science (right) stamps of a spurious hostless candidate detection. The top row shows the original stamps and the bottom row shows the masks produced from sigma clipping. We can see that the erroneous detection is driven by artifacts present in the original template stamp. As a result, sigma clipped template shown on the bottom left panel shows no signal. At the center of the stamps, we display a red circle of 7 pix radius that indicates the aperture radius of the associated photometry.</figcaption> </figure> </section> <section class="ltx_subsection" id="S3.SS3"> <h3 class="ltx_title ltx_title_subsection"> 3.3 Host categorization via Fourier power spectrum</h3> <div class="ltx_para" id="S3.SS3.p1"> To further examine the presence or absence of a host, if a transient is flagged as a hostless candidate by the sigma clipping method, ELEPHANT explores the Fourier space projections of the masked stamps. This strategy is reflective of methodologies previously applied to the classification of natural images across various landscapes <cite class="ltx_cite ltx_citemacro_citep">(Balboa & Grzywacz <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib4" title="">2003</a>)</cite>. By transforming the stamps into Fourier space, the pipeline is able to search for correlations in the background noise that can suggest the presence of a faint host, which would otherwise not be detected via the sigma clipping approach. This process involves calculating the medianized 1-dimensional power spectrum from the 2-dimensional Fourier transform of the images. The mathematical foundation of this method is laid out as follows: the Fourier transform, denoted by <math alttext="F(u,v)" class="ltx_Math" display="inline" id="S3.SS3.p1.1.m1.2"><semantics id="S3.SS3.p1.1.m1.2a"><mrow id="S3.SS3.p1.1.m1.2.3" xref="S3.SS3.p1.1.m1.2.3.cmml"><mi id="S3.SS3.p1.1.m1.2.3.2" xref="S3.SS3.p1.1.m1.2.3.2.cmml">F</mi><mo id="S3.SS3.p1.1.m1.2.3.1" xref="S3.SS3.p1.1.m1.2.3.1.cmml">⁢</mo><mrow id="S3.SS3.p1.1.m1.2.3.3.2" xref="S3.SS3.p1.1.m1.2.3.3.1.cmml"><mo id="S3.SS3.p1.1.m1.2.3.3.2.1" stretchy="false" xref="S3.SS3.p1.1.m1.2.3.3.1.cmml">(</mo><mi id="S3.SS3.p1.1.m1.1.1" xref="S3.SS3.p1.1.m1.1.1.cmml">u</mi><mo id="S3.SS3.p1.1.m1.2.3.3.2.2" xref="S3.SS3.p1.1.m1.2.3.3.1.cmml">,</mo><mi id="S3.SS3.p1.1.m1.2.2" xref="S3.SS3.p1.1.m1.2.2.cmml">v</mi><mo id="S3.SS3.p1.1.m1.2.3.3.2.3" stretchy="false" xref="S3.SS3.p1.1.m1.2.3.3.1.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS3.p1.1.m1.2b"><apply id="S3.SS3.p1.1.m1.2.3.cmml" xref="S3.SS3.p1.1.m1.2.3"><times id="S3.SS3.p1.1.m1.2.3.1.cmml" xref="S3.SS3.p1.1.m1.2.3.1"></times><ci id="S3.SS3.p1.1.m1.2.3.2.cmml" xref="S3.SS3.p1.1.m1.2.3.2">𝐹</ci><interval closure="open" id="S3.SS3.p1.1.m1.2.3.3.1.cmml" xref="S3.SS3.p1.1.m1.2.3.3.2"><ci id="S3.SS3.p1.1.m1.1.1.cmml" xref="S3.SS3.p1.1.m1.1.1">𝑢</ci><ci id="S3.SS3.p1.1.m1.2.2.cmml" xref="S3.SS3.p1.1.m1.2.2">𝑣</ci></interval></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p1.1.m1.2c">F(u,v)</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p1.1.m1.2d">italic_F ( italic_u , italic_v )</annotation></semantics></math>, of an image, <math alttext="I(x,y)" class="ltx_Math" display="inline" id="S3.SS3.p1.2.m2.2"><semantics id="S3.SS3.p1.2.m2.2a"><mrow id="S3.SS3.p1.2.m2.2.3" xref="S3.SS3.p1.2.m2.2.3.cmml"><mi id="S3.SS3.p1.2.m2.2.3.2" xref="S3.SS3.p1.2.m2.2.3.2.cmml">I</mi><mo id="S3.SS3.p1.2.m2.2.3.1" xref="S3.SS3.p1.2.m2.2.3.1.cmml">⁢</mo><mrow id="S3.SS3.p1.2.m2.2.3.3.2" xref="S3.SS3.p1.2.m2.2.3.3.1.cmml"><mo id="S3.SS3.p1.2.m2.2.3.3.2.1" stretchy="false" xref="S3.SS3.p1.2.m2.2.3.3.1.cmml">(</mo><mi id="S3.SS3.p1.2.m2.1.1" xref="S3.SS3.p1.2.m2.1.1.cmml">x</mi><mo id="S3.SS3.p1.2.m2.2.3.3.2.2" xref="S3.SS3.p1.2.m2.2.3.3.1.cmml">,</mo><mi id="S3.SS3.p1.2.m2.2.2" xref="S3.SS3.p1.2.m2.2.2.cmml">y</mi><mo id="S3.SS3.p1.2.m2.2.3.3.2.3" stretchy="false" xref="S3.SS3.p1.2.m2.2.3.3.1.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS3.p1.2.m2.2b"><apply id="S3.SS3.p1.2.m2.2.3.cmml" xref="S3.SS3.p1.2.m2.2.3"><times id="S3.SS3.p1.2.m2.2.3.1.cmml" xref="S3.SS3.p1.2.m2.2.3.1"></times><ci id="S3.SS3.p1.2.m2.2.3.2.cmml" xref="S3.SS3.p1.2.m2.2.3.2">𝐼</ci><interval closure="open" id="S3.SS3.p1.2.m2.2.3.3.1.cmml" xref="S3.SS3.p1.2.m2.2.3.3.2"><ci id="S3.SS3.p1.2.m2.1.1.cmml" xref="S3.SS3.p1.2.m2.1.1">𝑥</ci><ci id="S3.SS3.p1.2.m2.2.2.cmml" xref="S3.SS3.p1.2.m2.2.2">𝑦</ci></interval></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p1.2.m2.2c">I(x,y)</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p1.2.m2.2d">italic_I ( italic_x , italic_y )</annotation></semantics></math>, is calculated according to: <table class="ltx_equation ltx_eqn_table" id="S3.E1"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="F(u,v)=\mathcal{F}\{I(x,y)\}," class="ltx_Math" display="block" id="S3.E1.m1.5"><semantics id="S3.E1.m1.5a"><mrow id="S3.E1.m1.5.5.1" xref="S3.E1.m1.5.5.1.1.cmml"><mrow id="S3.E1.m1.5.5.1.1" xref="S3.E1.m1.5.5.1.1.cmml"><mrow id="S3.E1.m1.5.5.1.1.3" xref="S3.E1.m1.5.5.1.1.3.cmml"><mi id="S3.E1.m1.5.5.1.1.3.2" xref="S3.E1.m1.5.5.1.1.3.2.cmml">F</mi><mo id="S3.E1.m1.5.5.1.1.3.1" xref="S3.E1.m1.5.5.1.1.3.1.cmml">⁢</mo><mrow id="S3.E1.m1.5.5.1.1.3.3.2" xref="S3.E1.m1.5.5.1.1.3.3.1.cmml"><mo id="S3.E1.m1.5.5.1.1.3.3.2.1" stretchy="false" xref="S3.E1.m1.5.5.1.1.3.3.1.cmml">(</mo><mi id="S3.E1.m1.1.1" xref="S3.E1.m1.1.1.cmml">u</mi><mo id="S3.E1.m1.5.5.1.1.3.3.2.2" xref="S3.E1.m1.5.5.1.1.3.3.1.cmml">,</mo><mi id="S3.E1.m1.2.2" xref="S3.E1.m1.2.2.cmml">v</mi><mo id="S3.E1.m1.5.5.1.1.3.3.2.3" stretchy="false" xref="S3.E1.m1.5.5.1.1.3.3.1.cmml">)</mo></mrow></mrow><mo id="S3.E1.m1.5.5.1.1.2" xref="S3.E1.m1.5.5.1.1.2.cmml">=</mo><mrow id="S3.E1.m1.5.5.1.1.1" xref="S3.E1.m1.5.5.1.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.E1.m1.5.5.1.1.1.3" xref="S3.E1.m1.5.5.1.1.1.3.cmml">ℱ</mi><mo id="S3.E1.m1.5.5.1.1.1.2" xref="S3.E1.m1.5.5.1.1.1.2.cmml">⁢</mo><mrow id="S3.E1.m1.5.5.1.1.1.1.1" xref="S3.E1.m1.5.5.1.1.1.1.2.cmml"><mo id="S3.E1.m1.5.5.1.1.1.1.1.2" stretchy="false" xref="S3.E1.m1.5.5.1.1.1.1.2.cmml">{</mo><mrow id="S3.E1.m1.5.5.1.1.1.1.1.1" xref="S3.E1.m1.5.5.1.1.1.1.1.1.cmml"><mi id="S3.E1.m1.5.5.1.1.1.1.1.1.2" xref="S3.E1.m1.5.5.1.1.1.1.1.1.2.cmml">I</mi><mo id="S3.E1.m1.5.5.1.1.1.1.1.1.1" xref="S3.E1.m1.5.5.1.1.1.1.1.1.1.cmml">⁢</mo><mrow id="S3.E1.m1.5.5.1.1.1.1.1.1.3.2" xref="S3.E1.m1.5.5.1.1.1.1.1.1.3.1.cmml"><mo id="S3.E1.m1.5.5.1.1.1.1.1.1.3.2.1" stretchy="false" xref="S3.E1.m1.5.5.1.1.1.1.1.1.3.1.cmml">(</mo><mi id="S3.E1.m1.3.3" xref="S3.E1.m1.3.3.cmml">x</mi><mo id="S3.E1.m1.5.5.1.1.1.1.1.1.3.2.2" xref="S3.E1.m1.5.5.1.1.1.1.1.1.3.1.cmml">,</mo><mi id="S3.E1.m1.4.4" xref="S3.E1.m1.4.4.cmml">y</mi><mo id="S3.E1.m1.5.5.1.1.1.1.1.1.3.2.3" stretchy="false" xref="S3.E1.m1.5.5.1.1.1.1.1.1.3.1.cmml">)</mo></mrow></mrow><mo id="S3.E1.m1.5.5.1.1.1.1.1.3" stretchy="false" xref="S3.E1.m1.5.5.1.1.1.1.2.cmml">}</mo></mrow></mrow></mrow><mo id="S3.E1.m1.5.5.1.2" xref="S3.E1.m1.5.5.1.1.cmml">,</mo></mrow><annotation-xml encoding="MathML-Content" id="S3.E1.m1.5b"><apply id="S3.E1.m1.5.5.1.1.cmml" xref="S3.E1.m1.5.5.1"><eq id="S3.E1.m1.5.5.1.1.2.cmml" xref="S3.E1.m1.5.5.1.1.2"></eq><apply id="S3.E1.m1.5.5.1.1.3.cmml" xref="S3.E1.m1.5.5.1.1.3"><times id="S3.E1.m1.5.5.1.1.3.1.cmml" xref="S3.E1.m1.5.5.1.1.3.1"></times><ci id="S3.E1.m1.5.5.1.1.3.2.cmml" xref="S3.E1.m1.5.5.1.1.3.2">𝐹</ci><interval closure="open" id="S3.E1.m1.5.5.1.1.3.3.1.cmml" xref="S3.E1.m1.5.5.1.1.3.3.2"><ci id="S3.E1.m1.1.1.cmml" xref="S3.E1.m1.1.1">𝑢</ci><ci id="S3.E1.m1.2.2.cmml" xref="S3.E1.m1.2.2">𝑣</ci></interval></apply><apply id="S3.E1.m1.5.5.1.1.1.cmml" xref="S3.E1.m1.5.5.1.1.1"><times id="S3.E1.m1.5.5.1.1.1.2.cmml" xref="S3.E1.m1.5.5.1.1.1.2"></times><ci id="S3.E1.m1.5.5.1.1.1.3.cmml" xref="S3.E1.m1.5.5.1.1.1.3">ℱ</ci><set id="S3.E1.m1.5.5.1.1.1.1.2.cmml" xref="S3.E1.m1.5.5.1.1.1.1.1"><apply id="S3.E1.m1.5.5.1.1.1.1.1.1.cmml" xref="S3.E1.m1.5.5.1.1.1.1.1.1"><times id="S3.E1.m1.5.5.1.1.1.1.1.1.1.cmml" xref="S3.E1.m1.5.5.1.1.1.1.1.1.1"></times><ci id="S3.E1.m1.5.5.1.1.1.1.1.1.2.cmml" xref="S3.E1.m1.5.5.1.1.1.1.1.1.2">𝐼</ci><interval closure="open" id="S3.E1.m1.5.5.1.1.1.1.1.1.3.1.cmml" xref="S3.E1.m1.5.5.1.1.1.1.1.1.3.2"><ci id="S3.E1.m1.3.3.cmml" xref="S3.E1.m1.3.3">𝑥</ci><ci id="S3.E1.m1.4.4.cmml" xref="S3.E1.m1.4.4">𝑦</ci></interval></apply></set></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.E1.m1.5c">F(u,v)=\mathcal{F}\{I(x,y)\},</annotation><annotation encoding="application/x-llamapun" id="S3.E1.m1.5d">italic_F ( italic_u , italic_v ) = caligraphic_F { italic_I ( italic_x , italic_y ) } ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1">(1)</td> </tr></tbody> </table> where <math alttext="(x,y)" class="ltx_Math" display="inline" id="S3.SS3.p1.3.m1.2"><semantics id="S3.SS3.p1.3.m1.2a"><mrow id="S3.SS3.p1.3.m1.2.3.2" xref="S3.SS3.p1.3.m1.2.3.1.cmml"><mo id="S3.SS3.p1.3.m1.2.3.2.1" stretchy="false" xref="S3.SS3.p1.3.m1.2.3.1.cmml">(</mo><mi id="S3.SS3.p1.3.m1.1.1" xref="S3.SS3.p1.3.m1.1.1.cmml">x</mi><mo id="S3.SS3.p1.3.m1.2.3.2.2" xref="S3.SS3.p1.3.m1.2.3.1.cmml">,</mo><mi id="S3.SS3.p1.3.m1.2.2" xref="S3.SS3.p1.3.m1.2.2.cmml">y</mi><mo id="S3.SS3.p1.3.m1.2.3.2.3" stretchy="false" xref="S3.SS3.p1.3.m1.2.3.1.cmml">)</mo></mrow><annotation-xml encoding="MathML-Content" id="S3.SS3.p1.3.m1.2b"><interval closure="open" id="S3.SS3.p1.3.m1.2.3.1.cmml" xref="S3.SS3.p1.3.m1.2.3.2"><ci id="S3.SS3.p1.3.m1.1.1.cmml" xref="S3.SS3.p1.3.m1.1.1">𝑥</ci><ci id="S3.SS3.p1.3.m1.2.2.cmml" xref="S3.SS3.p1.3.m1.2.2">𝑦</ci></interval></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p1.3.m1.2c">(x,y)</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p1.3.m1.2d">( italic_x , italic_y )</annotation></semantics></math> represents the pixel coordinates and <math alttext="(u,v)" class="ltx_Math" display="inline" id="S3.SS3.p1.4.m2.2"><semantics id="S3.SS3.p1.4.m2.2a"><mrow id="S3.SS3.p1.4.m2.2.3.2" xref="S3.SS3.p1.4.m2.2.3.1.cmml"><mo id="S3.SS3.p1.4.m2.2.3.2.1" stretchy="false" xref="S3.SS3.p1.4.m2.2.3.1.cmml">(</mo><mi id="S3.SS3.p1.4.m2.1.1" xref="S3.SS3.p1.4.m2.1.1.cmml">u</mi><mo id="S3.SS3.p1.4.m2.2.3.2.2" xref="S3.SS3.p1.4.m2.2.3.1.cmml">,</mo><mi id="S3.SS3.p1.4.m2.2.2" xref="S3.SS3.p1.4.m2.2.2.cmml">v</mi><mo id="S3.SS3.p1.4.m2.2.3.2.3" stretchy="false" xref="S3.SS3.p1.4.m2.2.3.1.cmml">)</mo></mrow><annotation-xml encoding="MathML-Content" id="S3.SS3.p1.4.m2.2b"><interval closure="open" id="S3.SS3.p1.4.m2.2.3.1.cmml" xref="S3.SS3.p1.4.m2.2.3.2"><ci id="S3.SS3.p1.4.m2.1.1.cmml" xref="S3.SS3.p1.4.m2.1.1">𝑢</ci><ci id="S3.SS3.p1.4.m2.2.2.cmml" xref="S3.SS3.p1.4.m2.2.2">𝑣</ci></interval></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p1.4.m2.2c">(u,v)</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p1.4.m2.2d">( italic_u , italic_v )</annotation></semantics></math> the frequency domain coordinates. From this, the power spectrum, <math alttext="P(u,v)" class="ltx_Math" display="inline" id="S3.SS3.p1.5.m3.2"><semantics id="S3.SS3.p1.5.m3.2a"><mrow id="S3.SS3.p1.5.m3.2.3" xref="S3.SS3.p1.5.m3.2.3.cmml"><mi id="S3.SS3.p1.5.m3.2.3.2" xref="S3.SS3.p1.5.m3.2.3.2.cmml">P</mi><mo id="S3.SS3.p1.5.m3.2.3.1" xref="S3.SS3.p1.5.m3.2.3.1.cmml">⁢</mo><mrow id="S3.SS3.p1.5.m3.2.3.3.2" xref="S3.SS3.p1.5.m3.2.3.3.1.cmml"><mo id="S3.SS3.p1.5.m3.2.3.3.2.1" stretchy="false" xref="S3.SS3.p1.5.m3.2.3.3.1.cmml">(</mo><mi id="S3.SS3.p1.5.m3.1.1" xref="S3.SS3.p1.5.m3.1.1.cmml">u</mi><mo id="S3.SS3.p1.5.m3.2.3.3.2.2" xref="S3.SS3.p1.5.m3.2.3.3.1.cmml">,</mo><mi id="S3.SS3.p1.5.m3.2.2" xref="S3.SS3.p1.5.m3.2.2.cmml">v</mi><mo id="S3.SS3.p1.5.m3.2.3.3.2.3" stretchy="false" xref="S3.SS3.p1.5.m3.2.3.3.1.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS3.p1.5.m3.2b"><apply id="S3.SS3.p1.5.m3.2.3.cmml" xref="S3.SS3.p1.5.m3.2.3"><times id="S3.SS3.p1.5.m3.2.3.1.cmml" xref="S3.SS3.p1.5.m3.2.3.1"></times><ci id="S3.SS3.p1.5.m3.2.3.2.cmml" xref="S3.SS3.p1.5.m3.2.3.2">𝑃</ci><interval closure="open" id="S3.SS3.p1.5.m3.2.3.3.1.cmml" xref="S3.SS3.p1.5.m3.2.3.3.2"><ci id="S3.SS3.p1.5.m3.1.1.cmml" xref="S3.SS3.p1.5.m3.1.1">𝑢</ci><ci id="S3.SS3.p1.5.m3.2.2.cmml" xref="S3.SS3.p1.5.m3.2.2">𝑣</ci></interval></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p1.5.m3.2c">P(u,v)</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p1.5.m3.2d">italic_P ( italic_u , italic_v )</annotation></semantics></math>, is derived through the equation: <table class="ltx_equation ltx_eqn_table" id="S3.E2"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="P(u,v)=|F(u,v)|^{2}." class="ltx_Math" display="block" id="S3.E2.m1.5"><semantics id="S3.E2.m1.5a"><mrow id="S3.E2.m1.5.5.1" xref="S3.E2.m1.5.5.1.1.cmml"><mrow id="S3.E2.m1.5.5.1.1" xref="S3.E2.m1.5.5.1.1.cmml"><mrow id="S3.E2.m1.5.5.1.1.3" xref="S3.E2.m1.5.5.1.1.3.cmml"><mi id="S3.E2.m1.5.5.1.1.3.2" xref="S3.E2.m1.5.5.1.1.3.2.cmml">P</mi><mo id="S3.E2.m1.5.5.1.1.3.1" xref="S3.E2.m1.5.5.1.1.3.1.cmml">⁢</mo><mrow id="S3.E2.m1.5.5.1.1.3.3.2" xref="S3.E2.m1.5.5.1.1.3.3.1.cmml"><mo id="S3.E2.m1.5.5.1.1.3.3.2.1" stretchy="false" xref="S3.E2.m1.5.5.1.1.3.3.1.cmml">(</mo><mi id="S3.E2.m1.1.1" xref="S3.E2.m1.1.1.cmml">u</mi><mo id="S3.E2.m1.5.5.1.1.3.3.2.2" xref="S3.E2.m1.5.5.1.1.3.3.1.cmml">,</mo><mi id="S3.E2.m1.2.2" xref="S3.E2.m1.2.2.cmml">v</mi><mo id="S3.E2.m1.5.5.1.1.3.3.2.3" stretchy="false" xref="S3.E2.m1.5.5.1.1.3.3.1.cmml">)</mo></mrow></mrow><mo id="S3.E2.m1.5.5.1.1.2" xref="S3.E2.m1.5.5.1.1.2.cmml">=</mo><msup id="S3.E2.m1.5.5.1.1.1" xref="S3.E2.m1.5.5.1.1.1.cmml"><mrow id="S3.E2.m1.5.5.1.1.1.1.1" xref="S3.E2.m1.5.5.1.1.1.1.2.cmml"><mo id="S3.E2.m1.5.5.1.1.1.1.1.2" stretchy="false" xref="S3.E2.m1.5.5.1.1.1.1.2.1.cmml">|</mo><mrow id="S3.E2.m1.5.5.1.1.1.1.1.1" xref="S3.E2.m1.5.5.1.1.1.1.1.1.cmml"><mi id="S3.E2.m1.5.5.1.1.1.1.1.1.2" xref="S3.E2.m1.5.5.1.1.1.1.1.1.2.cmml">F</mi><mo id="S3.E2.m1.5.5.1.1.1.1.1.1.1" xref="S3.E2.m1.5.5.1.1.1.1.1.1.1.cmml">⁢</mo><mrow id="S3.E2.m1.5.5.1.1.1.1.1.1.3.2" xref="S3.E2.m1.5.5.1.1.1.1.1.1.3.1.cmml"><mo id="S3.E2.m1.5.5.1.1.1.1.1.1.3.2.1" stretchy="false" xref="S3.E2.m1.5.5.1.1.1.1.1.1.3.1.cmml">(</mo><mi id="S3.E2.m1.3.3" xref="S3.E2.m1.3.3.cmml">u</mi><mo id="S3.E2.m1.5.5.1.1.1.1.1.1.3.2.2" xref="S3.E2.m1.5.5.1.1.1.1.1.1.3.1.cmml">,</mo><mi id="S3.E2.m1.4.4" xref="S3.E2.m1.4.4.cmml">v</mi><mo id="S3.E2.m1.5.5.1.1.1.1.1.1.3.2.3" stretchy="false" xref="S3.E2.m1.5.5.1.1.1.1.1.1.3.1.cmml">)</mo></mrow></mrow><mo id="S3.E2.m1.5.5.1.1.1.1.1.3" stretchy="false" xref="S3.E2.m1.5.5.1.1.1.1.2.1.cmml">|</mo></mrow><mn id="S3.E2.m1.5.5.1.1.1.3" xref="S3.E2.m1.5.5.1.1.1.3.cmml">2</mn></msup></mrow><mo id="S3.E2.m1.5.5.1.2" lspace="0em" xref="S3.E2.m1.5.5.1.1.cmml">.</mo></mrow><annotation-xml encoding="MathML-Content" id="S3.E2.m1.5b"><apply id="S3.E2.m1.5.5.1.1.cmml" xref="S3.E2.m1.5.5.1"><eq id="S3.E2.m1.5.5.1.1.2.cmml" xref="S3.E2.m1.5.5.1.1.2"></eq><apply id="S3.E2.m1.5.5.1.1.3.cmml" xref="S3.E2.m1.5.5.1.1.3"><times id="S3.E2.m1.5.5.1.1.3.1.cmml" xref="S3.E2.m1.5.5.1.1.3.1"></times><ci id="S3.E2.m1.5.5.1.1.3.2.cmml" xref="S3.E2.m1.5.5.1.1.3.2">𝑃</ci><interval closure="open" id="S3.E2.m1.5.5.1.1.3.3.1.cmml" xref="S3.E2.m1.5.5.1.1.3.3.2"><ci id="S3.E2.m1.1.1.cmml" xref="S3.E2.m1.1.1">𝑢</ci><ci id="S3.E2.m1.2.2.cmml" xref="S3.E2.m1.2.2">𝑣</ci></interval></apply><apply id="S3.E2.m1.5.5.1.1.1.cmml" xref="S3.E2.m1.5.5.1.1.1"><csymbol cd="ambiguous" id="S3.E2.m1.5.5.1.1.1.2.cmml" xref="S3.E2.m1.5.5.1.1.1">superscript</csymbol><apply id="S3.E2.m1.5.5.1.1.1.1.2.cmml" xref="S3.E2.m1.5.5.1.1.1.1.1"><abs id="S3.E2.m1.5.5.1.1.1.1.2.1.cmml" xref="S3.E2.m1.5.5.1.1.1.1.1.2"></abs><apply id="S3.E2.m1.5.5.1.1.1.1.1.1.cmml" xref="S3.E2.m1.5.5.1.1.1.1.1.1"><times id="S3.E2.m1.5.5.1.1.1.1.1.1.1.cmml" xref="S3.E2.m1.5.5.1.1.1.1.1.1.1"></times><ci id="S3.E2.m1.5.5.1.1.1.1.1.1.2.cmml" xref="S3.E2.m1.5.5.1.1.1.1.1.1.2">𝐹</ci><interval closure="open" id="S3.E2.m1.5.5.1.1.1.1.1.1.3.1.cmml" xref="S3.E2.m1.5.5.1.1.1.1.1.1.3.2"><ci id="S3.E2.m1.3.3.cmml" xref="S3.E2.m1.3.3">𝑢</ci><ci id="S3.E2.m1.4.4.cmml" xref="S3.E2.m1.4.4">𝑣</ci></interval></apply></apply><cn id="S3.E2.m1.5.5.1.1.1.3.cmml" type="integer" xref="S3.E2.m1.5.5.1.1.1.3">2</cn></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.E2.m1.5c">P(u,v)=|F(u,v)|^{2}.</annotation><annotation encoding="application/x-llamapun" id="S3.E2.m1.5d">italic_P ( italic_u , italic_v ) = | italic_F ( italic_u , italic_v ) | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT .</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1">(2)</td> </tr></tbody> </table> The median power, <math alttext="M(k)" class="ltx_Math" display="inline" id="S3.SS3.p1.6.m1.1"><semantics id="S3.SS3.p1.6.m1.1a"><mrow id="S3.SS3.p1.6.m1.1.2" xref="S3.SS3.p1.6.m1.1.2.cmml"><mi id="S3.SS3.p1.6.m1.1.2.2" xref="S3.SS3.p1.6.m1.1.2.2.cmml">M</mi><mo id="S3.SS3.p1.6.m1.1.2.1" xref="S3.SS3.p1.6.m1.1.2.1.cmml">⁢</mo><mrow id="S3.SS3.p1.6.m1.1.2.3.2" xref="S3.SS3.p1.6.m1.1.2.cmml"><mo id="S3.SS3.p1.6.m1.1.2.3.2.1" stretchy="false" xref="S3.SS3.p1.6.m1.1.2.cmml">(</mo><mi id="S3.SS3.p1.6.m1.1.1" xref="S3.SS3.p1.6.m1.1.1.cmml">k</mi><mo id="S3.SS3.p1.6.m1.1.2.3.2.2" stretchy="false" xref="S3.SS3.p1.6.m1.1.2.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS3.p1.6.m1.1b"><apply id="S3.SS3.p1.6.m1.1.2.cmml" xref="S3.SS3.p1.6.m1.1.2"><times id="S3.SS3.p1.6.m1.1.2.1.cmml" xref="S3.SS3.p1.6.m1.1.2.1"></times><ci id="S3.SS3.p1.6.m1.1.2.2.cmml" xref="S3.SS3.p1.6.m1.1.2.2">𝑀</ci><ci id="S3.SS3.p1.6.m1.1.1.cmml" xref="S3.SS3.p1.6.m1.1.1">𝑘</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p1.6.m1.1c">M(k)</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p1.6.m1.1d">italic_M ( italic_k )</annotation></semantics></math>, for each radial frequency <math alttext="k=\sqrt{u^{2}+v^{2}}" class="ltx_Math" display="inline" id="S3.SS3.p1.7.m2.1"><semantics id="S3.SS3.p1.7.m2.1a"><mrow id="S3.SS3.p1.7.m2.1.1" xref="S3.SS3.p1.7.m2.1.1.cmml"><mi id="S3.SS3.p1.7.m2.1.1.2" xref="S3.SS3.p1.7.m2.1.1.2.cmml">k</mi><mo id="S3.SS3.p1.7.m2.1.1.1" xref="S3.SS3.p1.7.m2.1.1.1.cmml">=</mo><msqrt id="S3.SS3.p1.7.m2.1.1.3" xref="S3.SS3.p1.7.m2.1.1.3.cmml"><mrow id="S3.SS3.p1.7.m2.1.1.3.2" xref="S3.SS3.p1.7.m2.1.1.3.2.cmml"><msup id="S3.SS3.p1.7.m2.1.1.3.2.2" xref="S3.SS3.p1.7.m2.1.1.3.2.2.cmml"><mi id="S3.SS3.p1.7.m2.1.1.3.2.2.2" xref="S3.SS3.p1.7.m2.1.1.3.2.2.2.cmml">u</mi><mn id="S3.SS3.p1.7.m2.1.1.3.2.2.3" xref="S3.SS3.p1.7.m2.1.1.3.2.2.3.cmml">2</mn></msup><mo id="S3.SS3.p1.7.m2.1.1.3.2.1" xref="S3.SS3.p1.7.m2.1.1.3.2.1.cmml">+</mo><msup id="S3.SS3.p1.7.m2.1.1.3.2.3" xref="S3.SS3.p1.7.m2.1.1.3.2.3.cmml"><mi id="S3.SS3.p1.7.m2.1.1.3.2.3.2" xref="S3.SS3.p1.7.m2.1.1.3.2.3.2.cmml">v</mi><mn id="S3.SS3.p1.7.m2.1.1.3.2.3.3" xref="S3.SS3.p1.7.m2.1.1.3.2.3.3.cmml">2</mn></msup></mrow></msqrt></mrow><annotation-xml encoding="MathML-Content" id="S3.SS3.p1.7.m2.1b"><apply id="S3.SS3.p1.7.m2.1.1.cmml" xref="S3.SS3.p1.7.m2.1.1"><eq id="S3.SS3.p1.7.m2.1.1.1.cmml" xref="S3.SS3.p1.7.m2.1.1.1"></eq><ci id="S3.SS3.p1.7.m2.1.1.2.cmml" xref="S3.SS3.p1.7.m2.1.1.2">𝑘</ci><apply id="S3.SS3.p1.7.m2.1.1.3.cmml" xref="S3.SS3.p1.7.m2.1.1.3"><root id="S3.SS3.p1.7.m2.1.1.3a.cmml" xref="S3.SS3.p1.7.m2.1.1.3"></root><apply id="S3.SS3.p1.7.m2.1.1.3.2.cmml" xref="S3.SS3.p1.7.m2.1.1.3.2"><plus id="S3.SS3.p1.7.m2.1.1.3.2.1.cmml" xref="S3.SS3.p1.7.m2.1.1.3.2.1"></plus><apply id="S3.SS3.p1.7.m2.1.1.3.2.2.cmml" xref="S3.SS3.p1.7.m2.1.1.3.2.2"><csymbol cd="ambiguous" id="S3.SS3.p1.7.m2.1.1.3.2.2.1.cmml" xref="S3.SS3.p1.7.m2.1.1.3.2.2">superscript</csymbol><ci id="S3.SS3.p1.7.m2.1.1.3.2.2.2.cmml" xref="S3.SS3.p1.7.m2.1.1.3.2.2.2">𝑢</ci><cn id="S3.SS3.p1.7.m2.1.1.3.2.2.3.cmml" type="integer" xref="S3.SS3.p1.7.m2.1.1.3.2.2.3">2</cn></apply><apply id="S3.SS3.p1.7.m2.1.1.3.2.3.cmml" xref="S3.SS3.p1.7.m2.1.1.3.2.3"><csymbol cd="ambiguous" id="S3.SS3.p1.7.m2.1.1.3.2.3.1.cmml" xref="S3.SS3.p1.7.m2.1.1.3.2.3">superscript</csymbol><ci id="S3.SS3.p1.7.m2.1.1.3.2.3.2.cmml" xref="S3.SS3.p1.7.m2.1.1.3.2.3.2">𝑣</ci><cn id="S3.SS3.p1.7.m2.1.1.3.2.3.3.cmml" type="integer" xref="S3.SS3.p1.7.m2.1.1.3.2.3.3">2</cn></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p1.7.m2.1c">k=\sqrt{u^{2}+v^{2}}</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p1.7.m2.1d">italic_k = square-root start_ARG italic_u start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + italic_v start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG</annotation></semantics></math>, is calculated by taking the median of the power values across all angular coordinates <math alttext="\theta" class="ltx_Math" display="inline" id="S3.SS3.p1.8.m3.1"><semantics id="S3.SS3.p1.8.m3.1a"><mi id="S3.SS3.p1.8.m3.1.1" xref="S3.SS3.p1.8.m3.1.1.cmml">θ</mi><annotation-xml encoding="MathML-Content" id="S3.SS3.p1.8.m3.1b"><ci id="S3.SS3.p1.8.m3.1.1.cmml" xref="S3.SS3.p1.8.m3.1.1">𝜃</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p1.8.m3.1c">\theta</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p1.8.m3.1d">italic_θ</annotation></semantics></math> for a given power <math alttext="k" class="ltx_Math" display="inline" id="S3.SS3.p1.9.m4.1"><semantics id="S3.SS3.p1.9.m4.1a"><mi id="S3.SS3.p1.9.m4.1.1" xref="S3.SS3.p1.9.m4.1.1.cmml">k</mi><annotation-xml encoding="MathML-Content" id="S3.SS3.p1.9.m4.1b"><ci id="S3.SS3.p1.9.m4.1.1.cmml" xref="S3.SS3.p1.9.m4.1.1">𝑘</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p1.9.m4.1c">k</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p1.9.m4.1d">italic_k</annotation></semantics></math>: <table class="ltx_equation ltx_eqn_table" id="S3.E3"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="M(k)=\mathrm{median}\{P_{k}\}." class="ltx_Math" display="block" id="S3.E3.m1.2"><semantics id="S3.E3.m1.2a"><mrow id="S3.E3.m1.2.2.1" xref="S3.E3.m1.2.2.1.1.cmml"><mrow id="S3.E3.m1.2.2.1.1" xref="S3.E3.m1.2.2.1.1.cmml"><mrow id="S3.E3.m1.2.2.1.1.3" xref="S3.E3.m1.2.2.1.1.3.cmml"><mi id="S3.E3.m1.2.2.1.1.3.2" xref="S3.E3.m1.2.2.1.1.3.2.cmml">M</mi><mo id="S3.E3.m1.2.2.1.1.3.1" xref="S3.E3.m1.2.2.1.1.3.1.cmml">⁢</mo><mrow id="S3.E3.m1.2.2.1.1.3.3.2" xref="S3.E3.m1.2.2.1.1.3.cmml"><mo id="S3.E3.m1.2.2.1.1.3.3.2.1" stretchy="false" xref="S3.E3.m1.2.2.1.1.3.cmml">(</mo><mi id="S3.E3.m1.1.1" xref="S3.E3.m1.1.1.cmml">k</mi><mo id="S3.E3.m1.2.2.1.1.3.3.2.2" stretchy="false" xref="S3.E3.m1.2.2.1.1.3.cmml">)</mo></mrow></mrow><mo id="S3.E3.m1.2.2.1.1.2" xref="S3.E3.m1.2.2.1.1.2.cmml">=</mo><mrow id="S3.E3.m1.2.2.1.1.1" xref="S3.E3.m1.2.2.1.1.1.cmml"><mi id="S3.E3.m1.2.2.1.1.1.3" xref="S3.E3.m1.2.2.1.1.1.3.cmml">median</mi><mo id="S3.E3.m1.2.2.1.1.1.2" xref="S3.E3.m1.2.2.1.1.1.2.cmml">⁢</mo><mrow id="S3.E3.m1.2.2.1.1.1.1.1" xref="S3.E3.m1.2.2.1.1.1.1.2.cmml"><mo id="S3.E3.m1.2.2.1.1.1.1.1.2" stretchy="false" xref="S3.E3.m1.2.2.1.1.1.1.2.cmml">{</mo><msub id="S3.E3.m1.2.2.1.1.1.1.1.1" xref="S3.E3.m1.2.2.1.1.1.1.1.1.cmml"><mi id="S3.E3.m1.2.2.1.1.1.1.1.1.2" xref="S3.E3.m1.2.2.1.1.1.1.1.1.2.cmml">P</mi><mi id="S3.E3.m1.2.2.1.1.1.1.1.1.3" xref="S3.E3.m1.2.2.1.1.1.1.1.1.3.cmml">k</mi></msub><mo id="S3.E3.m1.2.2.1.1.1.1.1.3" stretchy="false" xref="S3.E3.m1.2.2.1.1.1.1.2.cmml">}</mo></mrow></mrow></mrow><mo id="S3.E3.m1.2.2.1.2" lspace="0em" xref="S3.E3.m1.2.2.1.1.cmml">.</mo></mrow><annotation-xml encoding="MathML-Content" id="S3.E3.m1.2b"><apply id="S3.E3.m1.2.2.1.1.cmml" xref="S3.E3.m1.2.2.1"><eq id="S3.E3.m1.2.2.1.1.2.cmml" xref="S3.E3.m1.2.2.1.1.2"></eq><apply id="S3.E3.m1.2.2.1.1.3.cmml" xref="S3.E3.m1.2.2.1.1.3"><times id="S3.E3.m1.2.2.1.1.3.1.cmml" xref="S3.E3.m1.2.2.1.1.3.1"></times><ci id="S3.E3.m1.2.2.1.1.3.2.cmml" xref="S3.E3.m1.2.2.1.1.3.2">𝑀</ci><ci id="S3.E3.m1.1.1.cmml" xref="S3.E3.m1.1.1">𝑘</ci></apply><apply id="S3.E3.m1.2.2.1.1.1.cmml" xref="S3.E3.m1.2.2.1.1.1"><times id="S3.E3.m1.2.2.1.1.1.2.cmml" xref="S3.E3.m1.2.2.1.1.1.2"></times><ci id="S3.E3.m1.2.2.1.1.1.3.cmml" xref="S3.E3.m1.2.2.1.1.1.3">median</ci><set id="S3.E3.m1.2.2.1.1.1.1.2.cmml" xref="S3.E3.m1.2.2.1.1.1.1.1"><apply id="S3.E3.m1.2.2.1.1.1.1.1.1.cmml" xref="S3.E3.m1.2.2.1.1.1.1.1.1"><csymbol cd="ambiguous" id="S3.E3.m1.2.2.1.1.1.1.1.1.1.cmml" xref="S3.E3.m1.2.2.1.1.1.1.1.1">subscript</csymbol><ci id="S3.E3.m1.2.2.1.1.1.1.1.1.2.cmml" xref="S3.E3.m1.2.2.1.1.1.1.1.1.2">𝑃</ci><ci id="S3.E3.m1.2.2.1.1.1.1.1.1.3.cmml" xref="S3.E3.m1.2.2.1.1.1.1.1.1.3">𝑘</ci></apply></set></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.E3.m1.2c">M(k)=\mathrm{median}\{P_{k}\}.</annotation><annotation encoding="application/x-llamapun" id="S3.E3.m1.2d">italic_M ( italic_k ) = roman_median { italic_P start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT } .</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1">(3)</td> </tr></tbody> </table> We assume that the power spectrum of an image containing even a faint host signal will distinguish itself from the power spectrum of another from which sources were removed and whose pixels have been randomly shuffled, and consequently does not contain any spatially coherent information to be extracted. </div> <figure class="ltx_figure" id="S3.F4"> <div class="ltx_flex_figure"> <div class="ltx_flex_cell ltx_flex_size_2"> <div class="ltx_block ltx_figure_panel ltx_minipage ltx_align_middle" id="S3.F4.1" style="width:303.5pt;"> <img alt="Refer to caption" class="ltx_graphics ltx_img_landscape" height="331" id="S3.F4.1.g1" src="x5.png" width="830"/> </div> </div> <div class="ltx_flex_cell ltx_flex_size_2"> <div class="ltx_block ltx_figure_panel ltx_minipage ltx_align_middle" id="S3.F4.2" style="width:130.1pt;"> <img alt="Refer to caption" class="ltx_graphics ltx_img_square" height="698" id="S3.F4.2.g1" src="x6.png" width="705"/> </div> </div> </div> <figcaption class="ltx_caption">Figure 4: Stages of the power spectrum analysis for a template with host (SN2017iuu / ZTF18aajwbhh). From left to right the panels show the template image, the mask and the mask populated with noise. The right-most panel shows the distribution of Wasserstein distances between the original template and shuffled noised masks (gray) and between random pairs of shuffled noised masks (rose). The distributions were generated using 1000 different shuffles of the noised masks within the central patch of 7 <math alttext="\times" class="ltx_Math" display="inline" id="S3.F4.4.m1.1"><semantics id="S3.F4.4.m1.1b"><mo id="S3.F4.4.m1.1.1" xref="S3.F4.4.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S3.F4.4.m1.1c"><times id="S3.F4.4.m1.1.1.cmml" xref="S3.F4.4.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S3.F4.4.m1.1d">\times</annotation><annotation encoding="application/x-llamapun" id="S3.F4.4.m1.1e">×</annotation></semantics></math> 7 pixels. </figcaption> </figure> <figure class="ltx_figure" id="S3.F5"> <div class="ltx_flex_figure"> <div class="ltx_flex_cell ltx_flex_size_2"> <div class="ltx_block ltx_figure_panel ltx_minipage ltx_align_middle" id="S3.F5.1" style="width:303.5pt;"> <img alt="Refer to caption" class="ltx_graphics ltx_img_landscape" height="339" id="S3.F5.1.g1" src="x7.png" width="831"/> </div> </div> <div class="ltx_flex_cell ltx_flex_size_2"> <div class="ltx_block ltx_figure_panel ltx_minipage ltx_align_middle" id="S3.F5.2" style="width:130.1pt;"> <img alt="Refer to caption" class="ltx_graphics ltx_img_square" height="195" id="S3.F5.2.g1" src="x8.png" width="197"/> </div> </div> </div> <figcaption class="ltx_caption">Figure 5: Stages of the power spectrum analysis for a hostless template (SN2022knm / ZTF22aakkmri). Panel descriptions are equivalent to those described in Figure <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.F4" title="Figure 4 ‣ 3.3 Host categorization via Fourier power spectrum ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4</a>.</figcaption> </figure> <div class="ltx_para" id="S3.SS3.p2"> To explore this, we first compute the power spectrum of the original image. Subsequently, we use the masks resulted from sigma clipping and fill masked sections with random noise sampled from the pixel value distribution of the masked image itself. The images are then cropped to three distinct sizes: 7 <math alttext="\times" class="ltx_Math" display="inline" id="S3.SS3.p2.1.m1.1"><semantics id="S3.SS3.p2.1.m1.1a"><mo id="S3.SS3.p2.1.m1.1.1" xref="S3.SS3.p2.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S3.SS3.p2.1.m1.1b"><times id="S3.SS3.p2.1.m1.1.1.cmml" xref="S3.SS3.p2.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p2.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p2.1.m1.1d">×</annotation></semantics></math> 7, 15 <math alttext="\times" class="ltx_Math" display="inline" id="S3.SS3.p2.2.m2.1"><semantics id="S3.SS3.p2.2.m2.1a"><mo id="S3.SS3.p2.2.m2.1.1" xref="S3.SS3.p2.2.m2.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S3.SS3.p2.2.m2.1b"><times id="S3.SS3.p2.2.m2.1.1.cmml" xref="S3.SS3.p2.2.m2.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p2.2.m2.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p2.2.m2.1d">×</annotation></semantics></math> 15, and 29 <math alttext="\times" class="ltx_Math" display="inline" id="S3.SS3.p2.3.m3.1"><semantics id="S3.SS3.p2.3.m3.1a"><mo id="S3.SS3.p2.3.m3.1.1" xref="S3.SS3.p2.3.m3.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S3.SS3.p2.3.m3.1b"><times id="S3.SS3.p2.3.m3.1.1.cmml" xref="S3.SS3.p2.3.m3.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p2.3.m3.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p2.3.m3.1d">×</annotation></semantics></math> 29 pixels, always with the center coinciding with the position of the transient. Afterwards, we randomly shuffle the pixel positions and the power spectrum is recalculated. This process is repeated 1000 times. The radially averaged 1D power spectrum of the original image is then compared to those of each shuffled iteration using the Wasserstein distance, <math alttext="W(p,q)" class="ltx_Math" display="inline" id="S3.SS3.p2.4.m4.2"><semantics id="S3.SS3.p2.4.m4.2a"><mrow id="S3.SS3.p2.4.m4.2.3" xref="S3.SS3.p2.4.m4.2.3.cmml"><mi id="S3.SS3.p2.4.m4.2.3.2" xref="S3.SS3.p2.4.m4.2.3.2.cmml">W</mi><mo id="S3.SS3.p2.4.m4.2.3.1" xref="S3.SS3.p2.4.m4.2.3.1.cmml">⁢</mo><mrow id="S3.SS3.p2.4.m4.2.3.3.2" xref="S3.SS3.p2.4.m4.2.3.3.1.cmml"><mo id="S3.SS3.p2.4.m4.2.3.3.2.1" stretchy="false" xref="S3.SS3.p2.4.m4.2.3.3.1.cmml">(</mo><mi id="S3.SS3.p2.4.m4.1.1" xref="S3.SS3.p2.4.m4.1.1.cmml">p</mi><mo id="S3.SS3.p2.4.m4.2.3.3.2.2" xref="S3.SS3.p2.4.m4.2.3.3.1.cmml">,</mo><mi id="S3.SS3.p2.4.m4.2.2" xref="S3.SS3.p2.4.m4.2.2.cmml">q</mi><mo id="S3.SS3.p2.4.m4.2.3.3.2.3" stretchy="false" xref="S3.SS3.p2.4.m4.2.3.3.1.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS3.p2.4.m4.2b"><apply id="S3.SS3.p2.4.m4.2.3.cmml" xref="S3.SS3.p2.4.m4.2.3"><times id="S3.SS3.p2.4.m4.2.3.1.cmml" xref="S3.SS3.p2.4.m4.2.3.1"></times><ci id="S3.SS3.p2.4.m4.2.3.2.cmml" xref="S3.SS3.p2.4.m4.2.3.2">𝑊</ci><interval closure="open" id="S3.SS3.p2.4.m4.2.3.3.1.cmml" xref="S3.SS3.p2.4.m4.2.3.3.2"><ci id="S3.SS3.p2.4.m4.1.1.cmml" xref="S3.SS3.p2.4.m4.1.1">𝑝</ci><ci id="S3.SS3.p2.4.m4.2.2.cmml" xref="S3.SS3.p2.4.m4.2.2">𝑞</ci></interval></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p2.4.m4.2c">W(p,q)</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p2.4.m4.2d">italic_W ( italic_p , italic_q )</annotation></semantics></math>: </div> <div class="ltx_para" id="S3.SS3.p3"> <table class="ltx_equation ltx_eqn_table" id="S3.E4"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="W(p,q)=\inf_{\gamma\in\Pi(p,q)}\int_{X\times Y}\|x-y\|\,d\gamma(x,y)," class="ltx_Math" display="block" id="S3.E4.m1.7"><semantics id="S3.E4.m1.7a"><mrow id="S3.E4.m1.7.7.1" xref="S3.E4.m1.7.7.1.1.cmml"><mrow id="S3.E4.m1.7.7.1.1" xref="S3.E4.m1.7.7.1.1.cmml"><mrow id="S3.E4.m1.7.7.1.1.3" xref="S3.E4.m1.7.7.1.1.3.cmml"><mi id="S3.E4.m1.7.7.1.1.3.2" xref="S3.E4.m1.7.7.1.1.3.2.cmml">W</mi><mo id="S3.E4.m1.7.7.1.1.3.1" xref="S3.E4.m1.7.7.1.1.3.1.cmml">⁢</mo><mrow id="S3.E4.m1.7.7.1.1.3.3.2" xref="S3.E4.m1.7.7.1.1.3.3.1.cmml"><mo id="S3.E4.m1.7.7.1.1.3.3.2.1" stretchy="false" xref="S3.E4.m1.7.7.1.1.3.3.1.cmml">(</mo><mi id="S3.E4.m1.3.3" xref="S3.E4.m1.3.3.cmml">p</mi><mo id="S3.E4.m1.7.7.1.1.3.3.2.2" xref="S3.E4.m1.7.7.1.1.3.3.1.cmml">,</mo><mi id="S3.E4.m1.4.4" xref="S3.E4.m1.4.4.cmml">q</mi><mo id="S3.E4.m1.7.7.1.1.3.3.2.3" stretchy="false" xref="S3.E4.m1.7.7.1.1.3.3.1.cmml">)</mo></mrow></mrow><mo id="S3.E4.m1.7.7.1.1.2" rspace="0.1389em" xref="S3.E4.m1.7.7.1.1.2.cmml">=</mo><mrow id="S3.E4.m1.7.7.1.1.1" xref="S3.E4.m1.7.7.1.1.1.cmml"><munder id="S3.E4.m1.7.7.1.1.1.2" xref="S3.E4.m1.7.7.1.1.1.2.cmml"><mo id="S3.E4.m1.7.7.1.1.1.2.2" lspace="0.1389em" movablelimits="false" rspace="0em" xref="S3.E4.m1.7.7.1.1.1.2.2.cmml">inf</mo><mrow id="S3.E4.m1.2.2.2" xref="S3.E4.m1.2.2.2.cmml"><mi id="S3.E4.m1.2.2.2.4" xref="S3.E4.m1.2.2.2.4.cmml">γ</mi><mo id="S3.E4.m1.2.2.2.3" xref="S3.E4.m1.2.2.2.3.cmml">∈</mo><mrow id="S3.E4.m1.2.2.2.5" xref="S3.E4.m1.2.2.2.5.cmml"><mi id="S3.E4.m1.2.2.2.5.2" mathvariant="normal" xref="S3.E4.m1.2.2.2.5.2.cmml">Π</mi><mo id="S3.E4.m1.2.2.2.5.1" xref="S3.E4.m1.2.2.2.5.1.cmml">⁢</mo><mrow id="S3.E4.m1.2.2.2.5.3.2" xref="S3.E4.m1.2.2.2.5.3.1.cmml"><mo id="S3.E4.m1.2.2.2.5.3.2.1" stretchy="false" xref="S3.E4.m1.2.2.2.5.3.1.cmml">(</mo><mi id="S3.E4.m1.1.1.1.1" xref="S3.E4.m1.1.1.1.1.cmml">p</mi><mo id="S3.E4.m1.2.2.2.5.3.2.2" xref="S3.E4.m1.2.2.2.5.3.1.cmml">,</mo><mi id="S3.E4.m1.2.2.2.2" xref="S3.E4.m1.2.2.2.2.cmml">q</mi><mo id="S3.E4.m1.2.2.2.5.3.2.3" stretchy="false" xref="S3.E4.m1.2.2.2.5.3.1.cmml">)</mo></mrow></mrow></mrow></munder><mrow id="S3.E4.m1.7.7.1.1.1.1" xref="S3.E4.m1.7.7.1.1.1.1.cmml"><msub id="S3.E4.m1.7.7.1.1.1.1.2" xref="S3.E4.m1.7.7.1.1.1.1.2.cmml"><mo id="S3.E4.m1.7.7.1.1.1.1.2.2" rspace="0em" xref="S3.E4.m1.7.7.1.1.1.1.2.2.cmml">∫</mo><mrow id="S3.E4.m1.7.7.1.1.1.1.2.3" xref="S3.E4.m1.7.7.1.1.1.1.2.3.cmml"><mi id="S3.E4.m1.7.7.1.1.1.1.2.3.2" xref="S3.E4.m1.7.7.1.1.1.1.2.3.2.cmml">X</mi><mo id="S3.E4.m1.7.7.1.1.1.1.2.3.1" lspace="0.222em" rspace="0.222em" xref="S3.E4.m1.7.7.1.1.1.1.2.3.1.cmml">×</mo><mi id="S3.E4.m1.7.7.1.1.1.1.2.3.3" xref="S3.E4.m1.7.7.1.1.1.1.2.3.3.cmml">Y</mi></mrow></msub><mrow id="S3.E4.m1.7.7.1.1.1.1.1" xref="S3.E4.m1.7.7.1.1.1.1.1.cmml"><mrow id="S3.E4.m1.7.7.1.1.1.1.1.1.1" xref="S3.E4.m1.7.7.1.1.1.1.1.1.2.cmml"><mo id="S3.E4.m1.7.7.1.1.1.1.1.1.1.2" stretchy="false" xref="S3.E4.m1.7.7.1.1.1.1.1.1.2.1.cmml">‖</mo><mrow id="S3.E4.m1.7.7.1.1.1.1.1.1.1.1" xref="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.cmml"><mi id="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.2" xref="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.2.cmml">x</mi><mo id="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.1" xref="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.1.cmml">−</mo><mi id="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.3" xref="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.3.cmml">y</mi></mrow><mo id="S3.E4.m1.7.7.1.1.1.1.1.1.1.3" stretchy="false" xref="S3.E4.m1.7.7.1.1.1.1.1.1.2.1.cmml">‖</mo></mrow><mo id="S3.E4.m1.7.7.1.1.1.1.1.2" lspace="0.170em" xref="S3.E4.m1.7.7.1.1.1.1.1.2.cmml">⁢</mo><mrow id="S3.E4.m1.7.7.1.1.1.1.1.3" xref="S3.E4.m1.7.7.1.1.1.1.1.3.cmml"><mo id="S3.E4.m1.7.7.1.1.1.1.1.3.1" rspace="0em" xref="S3.E4.m1.7.7.1.1.1.1.1.3.1.cmml">𝑑</mo><mi id="S3.E4.m1.7.7.1.1.1.1.1.3.2" xref="S3.E4.m1.7.7.1.1.1.1.1.3.2.cmml">γ</mi></mrow><mo id="S3.E4.m1.7.7.1.1.1.1.1.2a" xref="S3.E4.m1.7.7.1.1.1.1.1.2.cmml">⁢</mo><mrow id="S3.E4.m1.7.7.1.1.1.1.1.4.2" xref="S3.E4.m1.7.7.1.1.1.1.1.4.1.cmml"><mo id="S3.E4.m1.7.7.1.1.1.1.1.4.2.1" stretchy="false" xref="S3.E4.m1.7.7.1.1.1.1.1.4.1.cmml">(</mo><mi id="S3.E4.m1.5.5" xref="S3.E4.m1.5.5.cmml">x</mi><mo id="S3.E4.m1.7.7.1.1.1.1.1.4.2.2" xref="S3.E4.m1.7.7.1.1.1.1.1.4.1.cmml">,</mo><mi id="S3.E4.m1.6.6" xref="S3.E4.m1.6.6.cmml">y</mi><mo id="S3.E4.m1.7.7.1.1.1.1.1.4.2.3" stretchy="false" xref="S3.E4.m1.7.7.1.1.1.1.1.4.1.cmml">)</mo></mrow></mrow></mrow></mrow></mrow><mo id="S3.E4.m1.7.7.1.2" xref="S3.E4.m1.7.7.1.1.cmml">,</mo></mrow><annotation-xml encoding="MathML-Content" id="S3.E4.m1.7b"><apply id="S3.E4.m1.7.7.1.1.cmml" xref="S3.E4.m1.7.7.1"><eq id="S3.E4.m1.7.7.1.1.2.cmml" xref="S3.E4.m1.7.7.1.1.2"></eq><apply id="S3.E4.m1.7.7.1.1.3.cmml" xref="S3.E4.m1.7.7.1.1.3"><times id="S3.E4.m1.7.7.1.1.3.1.cmml" xref="S3.E4.m1.7.7.1.1.3.1"></times><ci id="S3.E4.m1.7.7.1.1.3.2.cmml" xref="S3.E4.m1.7.7.1.1.3.2">𝑊</ci><interval closure="open" id="S3.E4.m1.7.7.1.1.3.3.1.cmml" xref="S3.E4.m1.7.7.1.1.3.3.2"><ci id="S3.E4.m1.3.3.cmml" xref="S3.E4.m1.3.3">𝑝</ci><ci id="S3.E4.m1.4.4.cmml" xref="S3.E4.m1.4.4">𝑞</ci></interval></apply><apply id="S3.E4.m1.7.7.1.1.1.cmml" xref="S3.E4.m1.7.7.1.1.1"><apply id="S3.E4.m1.7.7.1.1.1.2.cmml" xref="S3.E4.m1.7.7.1.1.1.2"><csymbol cd="ambiguous" id="S3.E4.m1.7.7.1.1.1.2.1.cmml" xref="S3.E4.m1.7.7.1.1.1.2">subscript</csymbol><csymbol cd="latexml" id="S3.E4.m1.7.7.1.1.1.2.2.cmml" xref="S3.E4.m1.7.7.1.1.1.2.2">infimum</csymbol><apply id="S3.E4.m1.2.2.2.cmml" xref="S3.E4.m1.2.2.2"><in id="S3.E4.m1.2.2.2.3.cmml" xref="S3.E4.m1.2.2.2.3"></in><ci id="S3.E4.m1.2.2.2.4.cmml" xref="S3.E4.m1.2.2.2.4">𝛾</ci><apply id="S3.E4.m1.2.2.2.5.cmml" xref="S3.E4.m1.2.2.2.5"><times id="S3.E4.m1.2.2.2.5.1.cmml" xref="S3.E4.m1.2.2.2.5.1"></times><ci id="S3.E4.m1.2.2.2.5.2.cmml" xref="S3.E4.m1.2.2.2.5.2">Π</ci><interval closure="open" id="S3.E4.m1.2.2.2.5.3.1.cmml" xref="S3.E4.m1.2.2.2.5.3.2"><ci id="S3.E4.m1.1.1.1.1.cmml" xref="S3.E4.m1.1.1.1.1">𝑝</ci><ci id="S3.E4.m1.2.2.2.2.cmml" xref="S3.E4.m1.2.2.2.2">𝑞</ci></interval></apply></apply></apply><apply id="S3.E4.m1.7.7.1.1.1.1.cmml" xref="S3.E4.m1.7.7.1.1.1.1"><apply id="S3.E4.m1.7.7.1.1.1.1.2.cmml" xref="S3.E4.m1.7.7.1.1.1.1.2"><csymbol cd="ambiguous" id="S3.E4.m1.7.7.1.1.1.1.2.1.cmml" xref="S3.E4.m1.7.7.1.1.1.1.2">subscript</csymbol><int id="S3.E4.m1.7.7.1.1.1.1.2.2.cmml" xref="S3.E4.m1.7.7.1.1.1.1.2.2"></int><apply id="S3.E4.m1.7.7.1.1.1.1.2.3.cmml" xref="S3.E4.m1.7.7.1.1.1.1.2.3"><times id="S3.E4.m1.7.7.1.1.1.1.2.3.1.cmml" xref="S3.E4.m1.7.7.1.1.1.1.2.3.1"></times><ci id="S3.E4.m1.7.7.1.1.1.1.2.3.2.cmml" xref="S3.E4.m1.7.7.1.1.1.1.2.3.2">𝑋</ci><ci id="S3.E4.m1.7.7.1.1.1.1.2.3.3.cmml" xref="S3.E4.m1.7.7.1.1.1.1.2.3.3">𝑌</ci></apply></apply><apply id="S3.E4.m1.7.7.1.1.1.1.1.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1"><times id="S3.E4.m1.7.7.1.1.1.1.1.2.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1.2"></times><apply id="S3.E4.m1.7.7.1.1.1.1.1.1.2.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1.1.1"><csymbol cd="latexml" id="S3.E4.m1.7.7.1.1.1.1.1.1.2.1.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1.1.1.2">norm</csymbol><apply id="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1.1.1.1"><minus id="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.1.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.1"></minus><ci id="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.2.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.2">𝑥</ci><ci id="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.3.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1.1.1.1.3">𝑦</ci></apply></apply><apply id="S3.E4.m1.7.7.1.1.1.1.1.3.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1.3"><csymbol cd="latexml" id="S3.E4.m1.7.7.1.1.1.1.1.3.1.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1.3.1">differential-d</csymbol><ci id="S3.E4.m1.7.7.1.1.1.1.1.3.2.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1.3.2">𝛾</ci></apply><interval closure="open" id="S3.E4.m1.7.7.1.1.1.1.1.4.1.cmml" xref="S3.E4.m1.7.7.1.1.1.1.1.4.2"><ci id="S3.E4.m1.5.5.cmml" xref="S3.E4.m1.5.5">𝑥</ci><ci id="S3.E4.m1.6.6.cmml" xref="S3.E4.m1.6.6">𝑦</ci></interval></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.E4.m1.7c">W(p,q)=\inf_{\gamma\in\Pi(p,q)}\int_{X\times Y}\|x-y\|\,d\gamma(x,y),</annotation><annotation encoding="application/x-llamapun" id="S3.E4.m1.7d">italic_W ( italic_p , italic_q ) = roman_inf start_POSTSUBSCRIPT italic_γ ∈ roman_Π ( italic_p , italic_q ) end_POSTSUBSCRIPT ∫ start_POSTSUBSCRIPT italic_X × italic_Y end_POSTSUBSCRIPT ∥ italic_x - italic_y ∥ italic_d italic_γ ( italic_x , italic_y ) ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1">(4)</td> </tr></tbody> </table> </div> <div class="ltx_para ltx_noindent" id="S3.SS3.p4"> which measures the distance between the <math alttext="p" class="ltx_Math" display="inline" id="S3.SS3.p4.1.m1.1"><semantics id="S3.SS3.p4.1.m1.1a"><mi id="S3.SS3.p4.1.m1.1.1" xref="S3.SS3.p4.1.m1.1.1.cmml">p</mi><annotation-xml encoding="MathML-Content" id="S3.SS3.p4.1.m1.1b"><ci id="S3.SS3.p4.1.m1.1.1.cmml" xref="S3.SS3.p4.1.m1.1.1">𝑝</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p4.1.m1.1c">p</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p4.1.m1.1d">italic_p</annotation></semantics></math> and <math alttext="q" class="ltx_Math" display="inline" id="S3.SS3.p4.2.m2.1"><semantics id="S3.SS3.p4.2.m2.1a"><mi id="S3.SS3.p4.2.m2.1.1" xref="S3.SS3.p4.2.m2.1.1.cmml">q</mi><annotation-xml encoding="MathML-Content" id="S3.SS3.p4.2.m2.1b"><ci id="S3.SS3.p4.2.m2.1.1.cmml" xref="S3.SS3.p4.2.m2.1.1">𝑞</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p4.2.m2.1c">q</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p4.2.m2.1d">italic_q</annotation></semantics></math> distributions. The presence of a host, even if weak, is suggested if the distances from the original image’s power spectrum to those of the shuffled images are on average greater than the distances between the power spectra from shuffled images themselves (see right panel of Fig <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.F4" title="Figure 4 ‣ 3.3 Host categorization via Fourier power spectrum ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4</a> for an example of distance distributions when a host is present, and Fig <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.F5" title="Figure 5 ‣ 3.3 Host categorization via Fourier power spectrum ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">5</a> for an example of the distance distributions for a hostless candidate). </div> <div class="ltx_para" id="S3.SS3.p5"> This process yields a sample of 1000 distances for comparisons between the original image’s power spectrum and the power spectra of the shuffled images for each cutout size. The final step involves estimating the Kolmogorov-Smirnov (K-S) statistic to quantify the similarity between these two distributions of distances. The K-S statistic is calculated using the following equation: <table class="ltx_equation ltx_eqn_table" id="S3.E5"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="D=\sup_{x\in\mathbb{R}}|S_{1}(x)-S_{2}(x)|," class="ltx_Math" display="block" id="S3.E5.m1.3"><semantics id="S3.E5.m1.3a"><mrow id="S3.E5.m1.3.3.1" xref="S3.E5.m1.3.3.1.1.cmml"><mrow id="S3.E5.m1.3.3.1.1" xref="S3.E5.m1.3.3.1.1.cmml"><mi id="S3.E5.m1.3.3.1.1.3" xref="S3.E5.m1.3.3.1.1.3.cmml">D</mi><mo id="S3.E5.m1.3.3.1.1.2" rspace="0.1389em" xref="S3.E5.m1.3.3.1.1.2.cmml">=</mo><mrow id="S3.E5.m1.3.3.1.1.1" xref="S3.E5.m1.3.3.1.1.1.cmml"><munder id="S3.E5.m1.3.3.1.1.1.2" xref="S3.E5.m1.3.3.1.1.1.2.cmml"><mo id="S3.E5.m1.3.3.1.1.1.2.2" lspace="0.1389em" movablelimits="false" rspace="0em" xref="S3.E5.m1.3.3.1.1.1.2.2.cmml">sup</mo><mrow id="S3.E5.m1.3.3.1.1.1.2.3" xref="S3.E5.m1.3.3.1.1.1.2.3.cmml"><mi id="S3.E5.m1.3.3.1.1.1.2.3.2" xref="S3.E5.m1.3.3.1.1.1.2.3.2.cmml">x</mi><mo id="S3.E5.m1.3.3.1.1.1.2.3.1" xref="S3.E5.m1.3.3.1.1.1.2.3.1.cmml">∈</mo><mi id="S3.E5.m1.3.3.1.1.1.2.3.3" xref="S3.E5.m1.3.3.1.1.1.2.3.3.cmml">ℝ</mi></mrow></munder><mrow id="S3.E5.m1.3.3.1.1.1.1.1" xref="S3.E5.m1.3.3.1.1.1.1.2.cmml"><mo id="S3.E5.m1.3.3.1.1.1.1.1.2" stretchy="false" xref="S3.E5.m1.3.3.1.1.1.1.2.1.cmml">|</mo><mrow id="S3.E5.m1.3.3.1.1.1.1.1.1" xref="S3.E5.m1.3.3.1.1.1.1.1.1.cmml"><mrow id="S3.E5.m1.3.3.1.1.1.1.1.1.2" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.cmml"><msub id="S3.E5.m1.3.3.1.1.1.1.1.1.2.2" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.2.cmml"><mi id="S3.E5.m1.3.3.1.1.1.1.1.1.2.2.2" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.2.2.cmml">S</mi><mn id="S3.E5.m1.3.3.1.1.1.1.1.1.2.2.3" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.2.3.cmml">1</mn></msub><mo id="S3.E5.m1.3.3.1.1.1.1.1.1.2.1" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.1.cmml">⁢</mo><mrow id="S3.E5.m1.3.3.1.1.1.1.1.1.2.3.2" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.cmml"><mo id="S3.E5.m1.3.3.1.1.1.1.1.1.2.3.2.1" stretchy="false" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.cmml">(</mo><mi id="S3.E5.m1.1.1" xref="S3.E5.m1.1.1.cmml">x</mi><mo id="S3.E5.m1.3.3.1.1.1.1.1.1.2.3.2.2" stretchy="false" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.cmml">)</mo></mrow></mrow><mo id="S3.E5.m1.3.3.1.1.1.1.1.1.1" xref="S3.E5.m1.3.3.1.1.1.1.1.1.1.cmml">−</mo><mrow id="S3.E5.m1.3.3.1.1.1.1.1.1.3" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.cmml"><msub id="S3.E5.m1.3.3.1.1.1.1.1.1.3.2" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.2.cmml"><mi id="S3.E5.m1.3.3.1.1.1.1.1.1.3.2.2" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.2.2.cmml">S</mi><mn id="S3.E5.m1.3.3.1.1.1.1.1.1.3.2.3" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.2.3.cmml">2</mn></msub><mo id="S3.E5.m1.3.3.1.1.1.1.1.1.3.1" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.1.cmml">⁢</mo><mrow id="S3.E5.m1.3.3.1.1.1.1.1.1.3.3.2" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.cmml"><mo id="S3.E5.m1.3.3.1.1.1.1.1.1.3.3.2.1" stretchy="false" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.cmml">(</mo><mi id="S3.E5.m1.2.2" xref="S3.E5.m1.2.2.cmml">x</mi><mo id="S3.E5.m1.3.3.1.1.1.1.1.1.3.3.2.2" stretchy="false" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.cmml">)</mo></mrow></mrow></mrow><mo id="S3.E5.m1.3.3.1.1.1.1.1.3" stretchy="false" xref="S3.E5.m1.3.3.1.1.1.1.2.1.cmml">|</mo></mrow></mrow></mrow><mo id="S3.E5.m1.3.3.1.2" xref="S3.E5.m1.3.3.1.1.cmml">,</mo></mrow><annotation-xml encoding="MathML-Content" id="S3.E5.m1.3b"><apply id="S3.E5.m1.3.3.1.1.cmml" xref="S3.E5.m1.3.3.1"><eq id="S3.E5.m1.3.3.1.1.2.cmml" xref="S3.E5.m1.3.3.1.1.2"></eq><ci id="S3.E5.m1.3.3.1.1.3.cmml" xref="S3.E5.m1.3.3.1.1.3">𝐷</ci><apply id="S3.E5.m1.3.3.1.1.1.cmml" xref="S3.E5.m1.3.3.1.1.1"><apply id="S3.E5.m1.3.3.1.1.1.2.cmml" xref="S3.E5.m1.3.3.1.1.1.2"><csymbol cd="ambiguous" id="S3.E5.m1.3.3.1.1.1.2.1.cmml" xref="S3.E5.m1.3.3.1.1.1.2">subscript</csymbol><csymbol cd="latexml" id="S3.E5.m1.3.3.1.1.1.2.2.cmml" xref="S3.E5.m1.3.3.1.1.1.2.2">supremum</csymbol><apply id="S3.E5.m1.3.3.1.1.1.2.3.cmml" xref="S3.E5.m1.3.3.1.1.1.2.3"><in id="S3.E5.m1.3.3.1.1.1.2.3.1.cmml" xref="S3.E5.m1.3.3.1.1.1.2.3.1"></in><ci id="S3.E5.m1.3.3.1.1.1.2.3.2.cmml" xref="S3.E5.m1.3.3.1.1.1.2.3.2">𝑥</ci><ci id="S3.E5.m1.3.3.1.1.1.2.3.3.cmml" xref="S3.E5.m1.3.3.1.1.1.2.3.3">ℝ</ci></apply></apply><apply id="S3.E5.m1.3.3.1.1.1.1.2.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1"><abs id="S3.E5.m1.3.3.1.1.1.1.2.1.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.2"></abs><apply id="S3.E5.m1.3.3.1.1.1.1.1.1.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1"><minus id="S3.E5.m1.3.3.1.1.1.1.1.1.1.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1.1"></minus><apply id="S3.E5.m1.3.3.1.1.1.1.1.1.2.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2"><times id="S3.E5.m1.3.3.1.1.1.1.1.1.2.1.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.1"></times><apply id="S3.E5.m1.3.3.1.1.1.1.1.1.2.2.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.2"><csymbol cd="ambiguous" id="S3.E5.m1.3.3.1.1.1.1.1.1.2.2.1.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.2">subscript</csymbol><ci id="S3.E5.m1.3.3.1.1.1.1.1.1.2.2.2.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.2.2">𝑆</ci><cn id="S3.E5.m1.3.3.1.1.1.1.1.1.2.2.3.cmml" type="integer" xref="S3.E5.m1.3.3.1.1.1.1.1.1.2.2.3">1</cn></apply><ci id="S3.E5.m1.1.1.cmml" xref="S3.E5.m1.1.1">𝑥</ci></apply><apply id="S3.E5.m1.3.3.1.1.1.1.1.1.3.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3"><times id="S3.E5.m1.3.3.1.1.1.1.1.1.3.1.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.1"></times><apply id="S3.E5.m1.3.3.1.1.1.1.1.1.3.2.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.2"><csymbol cd="ambiguous" id="S3.E5.m1.3.3.1.1.1.1.1.1.3.2.1.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.2">subscript</csymbol><ci id="S3.E5.m1.3.3.1.1.1.1.1.1.3.2.2.cmml" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.2.2">𝑆</ci><cn id="S3.E5.m1.3.3.1.1.1.1.1.1.3.2.3.cmml" type="integer" xref="S3.E5.m1.3.3.1.1.1.1.1.1.3.2.3">2</cn></apply><ci id="S3.E5.m1.2.2.cmml" xref="S3.E5.m1.2.2">𝑥</ci></apply></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.E5.m1.3c">D=\sup_{x\in\mathbb{R}}|S_{1}(x)-S_{2}(x)|,</annotation><annotation encoding="application/x-llamapun" id="S3.E5.m1.3d">italic_D = roman_sup start_POSTSUBSCRIPT italic_x ∈ blackboard_R end_POSTSUBSCRIPT | italic_S start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ( italic_x ) - italic_S start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( italic_x ) | ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1">(5)</td> </tr></tbody> </table> where <math alttext="D" class="ltx_Math" display="inline" id="S3.SS3.p5.1.m1.1"><semantics id="S3.SS3.p5.1.m1.1a"><mi id="S3.SS3.p5.1.m1.1.1" xref="S3.SS3.p5.1.m1.1.1.cmml">D</mi><annotation-xml encoding="MathML-Content" id="S3.SS3.p5.1.m1.1b"><ci id="S3.SS3.p5.1.m1.1.1.cmml" xref="S3.SS3.p5.1.m1.1.1">𝐷</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p5.1.m1.1c">D</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p5.1.m1.1d">italic_D</annotation></semantics></math> quantifies the maximum discrepancy between the cumulative distribution functions (CDFs) of two distinct samples. Here, <math alttext="S_{1}(x)" class="ltx_Math" display="inline" id="S3.SS3.p5.2.m2.1"><semantics id="S3.SS3.p5.2.m2.1a"><mrow id="S3.SS3.p5.2.m2.1.2" xref="S3.SS3.p5.2.m2.1.2.cmml"><msub id="S3.SS3.p5.2.m2.1.2.2" xref="S3.SS3.p5.2.m2.1.2.2.cmml"><mi id="S3.SS3.p5.2.m2.1.2.2.2" xref="S3.SS3.p5.2.m2.1.2.2.2.cmml">S</mi><mn id="S3.SS3.p5.2.m2.1.2.2.3" xref="S3.SS3.p5.2.m2.1.2.2.3.cmml">1</mn></msub><mo id="S3.SS3.p5.2.m2.1.2.1" xref="S3.SS3.p5.2.m2.1.2.1.cmml">⁢</mo><mrow id="S3.SS3.p5.2.m2.1.2.3.2" xref="S3.SS3.p5.2.m2.1.2.cmml"><mo id="S3.SS3.p5.2.m2.1.2.3.2.1" stretchy="false" xref="S3.SS3.p5.2.m2.1.2.cmml">(</mo><mi id="S3.SS3.p5.2.m2.1.1" xref="S3.SS3.p5.2.m2.1.1.cmml">x</mi><mo id="S3.SS3.p5.2.m2.1.2.3.2.2" stretchy="false" xref="S3.SS3.p5.2.m2.1.2.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS3.p5.2.m2.1b"><apply id="S3.SS3.p5.2.m2.1.2.cmml" xref="S3.SS3.p5.2.m2.1.2"><times id="S3.SS3.p5.2.m2.1.2.1.cmml" xref="S3.SS3.p5.2.m2.1.2.1"></times><apply id="S3.SS3.p5.2.m2.1.2.2.cmml" xref="S3.SS3.p5.2.m2.1.2.2"><csymbol cd="ambiguous" id="S3.SS3.p5.2.m2.1.2.2.1.cmml" xref="S3.SS3.p5.2.m2.1.2.2">subscript</csymbol><ci id="S3.SS3.p5.2.m2.1.2.2.2.cmml" xref="S3.SS3.p5.2.m2.1.2.2.2">𝑆</ci><cn id="S3.SS3.p5.2.m2.1.2.2.3.cmml" type="integer" xref="S3.SS3.p5.2.m2.1.2.2.3">1</cn></apply><ci id="S3.SS3.p5.2.m2.1.1.cmml" xref="S3.SS3.p5.2.m2.1.1">𝑥</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p5.2.m2.1c">S_{1}(x)</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p5.2.m2.1d">italic_S start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ( italic_x )</annotation></semantics></math> represents the empirical cumulative distribution function (ECDF) for the first sample, which consists of the Wasserstein distances between the power spectrum of the original image and those derived from shuffled images. <math alttext="S_{2}(x)" class="ltx_Math" display="inline" id="S3.SS3.p5.3.m3.1"><semantics id="S3.SS3.p5.3.m3.1a"><mrow id="S3.SS3.p5.3.m3.1.2" xref="S3.SS3.p5.3.m3.1.2.cmml"><msub id="S3.SS3.p5.3.m3.1.2.2" xref="S3.SS3.p5.3.m3.1.2.2.cmml"><mi id="S3.SS3.p5.3.m3.1.2.2.2" xref="S3.SS3.p5.3.m3.1.2.2.2.cmml">S</mi><mn id="S3.SS3.p5.3.m3.1.2.2.3" xref="S3.SS3.p5.3.m3.1.2.2.3.cmml">2</mn></msub><mo id="S3.SS3.p5.3.m3.1.2.1" xref="S3.SS3.p5.3.m3.1.2.1.cmml">⁢</mo><mrow id="S3.SS3.p5.3.m3.1.2.3.2" xref="S3.SS3.p5.3.m3.1.2.cmml"><mo id="S3.SS3.p5.3.m3.1.2.3.2.1" stretchy="false" xref="S3.SS3.p5.3.m3.1.2.cmml">(</mo><mi id="S3.SS3.p5.3.m3.1.1" xref="S3.SS3.p5.3.m3.1.1.cmml">x</mi><mo id="S3.SS3.p5.3.m3.1.2.3.2.2" stretchy="false" xref="S3.SS3.p5.3.m3.1.2.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS3.p5.3.m3.1b"><apply id="S3.SS3.p5.3.m3.1.2.cmml" xref="S3.SS3.p5.3.m3.1.2"><times id="S3.SS3.p5.3.m3.1.2.1.cmml" xref="S3.SS3.p5.3.m3.1.2.1"></times><apply id="S3.SS3.p5.3.m3.1.2.2.cmml" xref="S3.SS3.p5.3.m3.1.2.2"><csymbol cd="ambiguous" id="S3.SS3.p5.3.m3.1.2.2.1.cmml" xref="S3.SS3.p5.3.m3.1.2.2">subscript</csymbol><ci id="S3.SS3.p5.3.m3.1.2.2.2.cmml" xref="S3.SS3.p5.3.m3.1.2.2.2">𝑆</ci><cn id="S3.SS3.p5.3.m3.1.2.2.3.cmml" type="integer" xref="S3.SS3.p5.3.m3.1.2.2.3">2</cn></apply><ci id="S3.SS3.p5.3.m3.1.1.cmml" xref="S3.SS3.p5.3.m3.1.1">𝑥</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p5.3.m3.1c">S_{2}(x)</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p5.3.m3.1d">italic_S start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( italic_x )</annotation></semantics></math>, on the other hand, corresponds to the ECDF of the second sample, namely the distribution of distances among the shuffled images themselves. We use <math alttext="D" class="ltx_Math" display="inline" id="S3.SS3.p5.4.m4.1"><semantics id="S3.SS3.p5.4.m4.1a"><mi id="S3.SS3.p5.4.m4.1.1" xref="S3.SS3.p5.4.m4.1.1.cmml">D</mi><annotation-xml encoding="MathML-Content" id="S3.SS3.p5.4.m4.1b"><ci id="S3.SS3.p5.4.m4.1.1.cmml" xref="S3.SS3.p5.4.m4.1.1">𝐷</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.SS3.p5.4.m4.1c">D</annotation><annotation encoding="application/x-llamapun" id="S3.SS3.p5.4.m4.1d">italic_D</annotation></semantics></math> as a proxy for identifying the presence of a faint host in all images which survived the sigma clipping selection. </div> </section> </section> <section class="ltx_section" id="S4"> <h2 class="ltx_title ltx_title_section"> 4 Results</h2> <div class="ltx_para" id="S4.p1"> ELEPHANT combines 2 stages of filtering. All objects flagged as potential hostless candidates by the sigma clipping step (Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.SS2" title="3.2 Segmentation masks ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3.2</a>) were submitted to the power spectrum analysis (Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.SS3" title="3.3 Host categorization via Fourier power spectrum ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3.3</a>). This last stage attached to each object a K-S statistic value, <math alttext="D" class="ltx_Math" display="inline" id="S4.p1.1.m1.1"><semantics id="S4.p1.1.m1.1a"><mi id="S4.p1.1.m1.1.1" xref="S4.p1.1.m1.1.1.cmml">D</mi><annotation-xml encoding="MathML-Content" id="S4.p1.1.m1.1b"><ci id="S4.p1.1.m1.1.1.cmml" xref="S4.p1.1.m1.1.1">𝐷</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.p1.1.m1.1c">D</annotation><annotation encoding="application/x-llamapun" id="S4.p1.1.m1.1d">italic_D</annotation></semantics></math>, which was constructed as a proxy indicating the presence of a faint host. We used a subset of visually inspected objects to define a selection cut threshold based on <math alttext="D" class="ltx_Math" display="inline" id="S4.p1.2.m2.1"><semantics id="S4.p1.2.m2.1a"><mi id="S4.p1.2.m2.1.1" xref="S4.p1.2.m2.1.1.cmml">D</mi><annotation-xml encoding="MathML-Content" id="S4.p1.2.m2.1b"><ci id="S4.p1.2.m2.1.1.cmml" xref="S4.p1.2.m2.1.1">𝐷</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.p1.2.m2.1c">D</annotation><annotation encoding="application/x-llamapun" id="S4.p1.2.m2.1d">italic_D</annotation></semantics></math> (Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.SS1" title="4.1 𝐷 threshold for hostless candidates ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4.1</a>), and analyzed the results from imposing such a threshold on a subset of spectroscopically confirmed transients (Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.SS2" title="4.2 Hostless sources on TNS ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4.2</a>). </div> <section class="ltx_subsection" id="S4.SS1"> <h3 class="ltx_title ltx_title_subsection"> 4.1 <math alttext="D" class="ltx_Math" display="inline" id="S4.SS1.1.m1.1"><semantics id="S4.SS1.1.m1.1b"><mi id="S4.SS1.1.m1.1.1" xref="S4.SS1.1.m1.1.1.cmml">D</mi><annotation-xml encoding="MathML-Content" id="S4.SS1.1.m1.1c"><ci id="S4.SS1.1.m1.1.1.cmml" xref="S4.SS1.1.m1.1.1">𝐷</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.SS1.1.m1.1d">D</annotation><annotation encoding="application/x-llamapun" id="S4.SS1.1.m1.1e">italic_D</annotation></semantics></math> threshold for hostless candidates</h3> <figure class="ltx_figure" id="S4.F6"><img alt="Refer to caption" class="ltx_graphics ltx_img_square" height="739" id="S4.F6.g1" src="x9.png" width="830"/> <figcaption class="ltx_caption">Figure 6: Central panel: comparison between spectral classification reported on TNS (horizontal axis) and the classification reported by Fink obtained from other sources (vertical axis). The <math alttext="x" class="ltx_Math" display="inline" id="S4.F6.3.m1.1"><semantics id="S4.F6.3.m1.1b"><mi id="S4.F6.3.m1.1.1" xref="S4.F6.3.m1.1.1.cmml">x</mi><annotation-xml encoding="MathML-Content" id="S4.F6.3.m1.1c"><ci id="S4.F6.3.m1.1.1.cmml" xref="S4.F6.3.m1.1.1">𝑥</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.F6.3.m1.1d">x</annotation><annotation encoding="application/x-llamapun" id="S4.F6.3.m1.1e">italic_x</annotation></semantics></math> and <math alttext="y" class="ltx_Math" display="inline" id="S4.F6.4.m2.1"><semantics id="S4.F6.4.m2.1b"><mi id="S4.F6.4.m2.1.1" xref="S4.F6.4.m2.1.1.cmml">y</mi><annotation-xml encoding="MathML-Content" id="S4.F6.4.m2.1c"><ci id="S4.F6.4.m2.1.1.cmml" xref="S4.F6.4.m2.1.1">𝑦</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.F6.4.m2.1d">y</annotation><annotation encoding="application/x-llamapun" id="S4.F6.4.m2.1e">italic_y</annotation></semantics></math> axis side panels show the number of transients considered to be hostless by the sigma clipping method before applying the power spectrum (PS) analysis (orange), and the number of surviving hostless candidates after applying the PS analysis (blue).</figcaption> </figure> <figure class="ltx_figure" id="S4.F7"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="173" id="S4.F7.g1" src="x10.png" width="830"/> <figcaption class="ltx_caption ltx_centering">Figure 7: Distributions of the Kolmogorov-Smirnov statistic for the 181 objects with TNS classifications. The two categories, with host (orange) and hostless (blue) were identified through visual inspection. Panels show distributions obtained through the power spectrum analysis (Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.SS3" title="3.3 Host categorization via Fourier power spectrum ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3.3</a>) for different image sizes.</figcaption> </figure> <div class="ltx_para" id="S4.SS1.p1"> After applying the segmentation mask module (see Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.SS2" title="3.2 Segmentation masks ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3.2</a>), ELEPHANT finds 1669 hostless candidates, 181 of these have an associated spectroscopic classification available on TNS. Fig. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.F6" title="Figure 6 ‣ 4.1 𝐷 threshold for hostless candidates ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">6</a> compares the TNS classification (horizontal axis) against the classes found on SIMBAD (SN*_candidate, GinCl, SN and Unknown) or inferred via Fink classifiers (Microlensing candidate and SN candidate). We can see that most of these hostless candidates were classified as SN candidate by the ML classifiers, which is consistent with the final spectroscopic classification available on TNS. </div> <div class="ltx_para" id="S4.SS1.p2"> The stamps associated with the 181 hostless candidates with a TNS classification were visually inspected using the Aladin sky atlas999<a class="ltx_ref ltx_url ltx_font_typewriter" href="https://aladin.cds.unistra.fr/" title="">https://aladin.cds.unistra.fr/</a> <cite class="ltx_cite ltx_citemacro_citep">(Bonnarel et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib10" title="">2000</a>)</cite>. We were not able to visually identify a host for 118 candidates, thus we confirm them as hostless candidates. The remaining 63 events are considered to be contaminants. Figure <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.F7" title="Figure 7 ‣ 4.1 𝐷 threshold for hostless candidates ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">7</a> shows the distribution of the K-S statistic, <math alttext="D" class="ltx_Math" display="inline" id="S4.SS1.p2.1.m1.1"><semantics id="S4.SS1.p2.1.m1.1a"><mi id="S4.SS1.p2.1.m1.1.1" xref="S4.SS1.p2.1.m1.1.1.cmml">D</mi><annotation-xml encoding="MathML-Content" id="S4.SS1.p2.1.m1.1b"><ci id="S4.SS1.p2.1.m1.1.1.cmml" xref="S4.SS1.p2.1.m1.1.1">𝐷</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.SS1.p2.1.m1.1c">D</annotation><annotation encoding="application/x-llamapun" id="S4.SS1.p2.1.m1.1d">italic_D</annotation></semantics></math>, for the three considered cropped cutout sizes (see Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.SS3" title="3.3 Host categorization via Fourier power spectrum ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3.3</a>), for both classes, confirmed hostless candidates and contaminants with host. We used the distribution of the hostless candidates to empirically define a threshold that would enclose a minimum of 75% of the hostless events. Table <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.T1" title="Table 1 ‣ 4.1 𝐷 threshold for hostless candidates ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">1</a> shows the 75th percentile for each image size. Aiming at a low contamination level with 75% completeness, we chose to use the 15 <math alttext="\times" class="ltx_Math" display="inline" id="S4.SS1.p2.2.m2.1"><semantics id="S4.SS1.p2.2.m2.1a"><mo id="S4.SS1.p2.2.m2.1.1" xref="S4.SS1.p2.2.m2.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S4.SS1.p2.2.m2.1b"><times id="S4.SS1.p2.2.m2.1.1.cmml" xref="S4.SS1.p2.2.m2.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S4.SS1.p2.2.m2.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S4.SS1.p2.2.m2.1d">×</annotation></semantics></math> 15 pixel images and imposed a threshold of K-S statistic <math alttext="D<" class="ltx_Math" display="inline" id="S4.SS1.p2.3.m3.1"><semantics id="S4.SS1.p2.3.m3.1a"><mrow id="S4.SS1.p2.3.m3.1.1" xref="S4.SS1.p2.3.m3.1.1.cmml"><mi id="S4.SS1.p2.3.m3.1.1.2" xref="S4.SS1.p2.3.m3.1.1.2.cmml">D</mi><mo id="S4.SS1.p2.3.m3.1.1.1" xref="S4.SS1.p2.3.m3.1.1.1.cmml"><</mo><mi id="S4.SS1.p2.3.m3.1.1.3" xref="S4.SS1.p2.3.m3.1.1.3.cmml"></mi></mrow><annotation-xml encoding="MathML-Content" id="S4.SS1.p2.3.m3.1b"><apply id="S4.SS1.p2.3.m3.1.1.cmml" xref="S4.SS1.p2.3.m3.1.1"><lt id="S4.SS1.p2.3.m3.1.1.1.cmml" xref="S4.SS1.p2.3.m3.1.1.1"></lt><ci id="S4.SS1.p2.3.m3.1.1.2.cmml" xref="S4.SS1.p2.3.m3.1.1.2">𝐷</ci><csymbol cd="latexml" id="S4.SS1.p2.3.m3.1.1.3.cmml" xref="S4.SS1.p2.3.m3.1.1.3">absent</csymbol></apply></annotation-xml><annotation encoding="application/x-tex" id="S4.SS1.p2.3.m3.1c">D<</annotation><annotation encoding="application/x-llamapun" id="S4.SS1.p2.3.m3.1d">italic_D <</annotation></semantics></math> 0.5. Thus, we classify all objects with a K-S statistic below the threshold in either the template or the science image as hostless candidates. The last column of Table <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.T1" title="Table 1 ‣ 4.1 𝐷 threshold for hostless candidates ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">1</a> shows the resulting contamination when the threshold is applied. We note that the output of ELEPHANT is the <math alttext="D" class="ltx_Math" display="inline" id="S4.SS1.p2.4.m4.1"><semantics id="S4.SS1.p2.4.m4.1a"><mi id="S4.SS1.p2.4.m4.1.1" xref="S4.SS1.p2.4.m4.1.1.cmml">D</mi><annotation-xml encoding="MathML-Content" id="S4.SS1.p2.4.m4.1b"><ci id="S4.SS1.p2.4.m4.1.1.cmml" xref="S4.SS1.p2.4.m4.1.1">𝐷</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.SS1.p2.4.m4.1c">D</annotation><annotation encoding="application/x-llamapun" id="S4.SS1.p2.4.m4.1d">italic_D</annotation></semantics></math> value, and the user could employ a different threshold to select hostless candidates. In particular, the threshold could be further adjusted once more events are confirmed to be hostless. </div> <figure class="ltx_table" id="S4.T1"> <table class="ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle" id="S4.T1.3"> <thead class="ltx_thead"> <tr class="ltx_tr" id="S4.T1.3.4.1"> <th class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row ltx_border_r" id="S4.T1.3.4.1.1">Image size (pix)</th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r" id="S4.T1.3.4.1.2">K-S threshold</th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column" id="S4.T1.3.4.1.3">Contamination (%) </th> </tr> </thead> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="S4.T1.1.1"> <th class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S4.T1.1.1.1"> 7 <math alttext="\times" class="ltx_Math" display="inline" id="S4.T1.1.1.1.m1.1"><semantics id="S4.T1.1.1.1.m1.1a"><mo id="S4.T1.1.1.1.m1.1.1" xref="S4.T1.1.1.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S4.T1.1.1.1.m1.1b"><times id="S4.T1.1.1.1.m1.1.1.cmml" xref="S4.T1.1.1.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S4.T1.1.1.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S4.T1.1.1.1.m1.1d">×</annotation></semantics></math> 7</th> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S4.T1.1.1.2">0.25</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S4.T1.1.1.3">27.01</td> </tr> <tr class="ltx_tr" id="S4.T1.2.2"> <th class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" id="S4.T1.2.2.1">15 <math alttext="\times" class="ltx_Math" display="inline" id="S4.T1.2.2.1.m1.1"><semantics id="S4.T1.2.2.1.m1.1a"><mo id="S4.T1.2.2.1.m1.1.1" xref="S4.T1.2.2.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S4.T1.2.2.1.m1.1b"><times id="S4.T1.2.2.1.m1.1.1.cmml" xref="S4.T1.2.2.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S4.T1.2.2.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S4.T1.2.2.1.m1.1d">×</annotation></semantics></math> 15</th> <td class="ltx_td ltx_align_center ltx_border_r" id="S4.T1.2.2.2">0.50</td> <td class="ltx_td ltx_align_center" id="S4.T1.2.2.3">25.97</td> </tr> <tr class="ltx_tr" id="S4.T1.3.3"> <th class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" id="S4.T1.3.3.1">29 <math alttext="\times" class="ltx_Math" display="inline" id="S4.T1.3.3.1.m1.1"><semantics id="S4.T1.3.3.1.m1.1a"><mo id="S4.T1.3.3.1.m1.1.1" xref="S4.T1.3.3.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S4.T1.3.3.1.m1.1b"><times id="S4.T1.3.3.1.m1.1.1.cmml" xref="S4.T1.3.3.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S4.T1.3.3.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S4.T1.3.3.1.m1.1d">×</annotation></semantics></math> 29</th> <td class="ltx_td ltx_align_center ltx_border_r" id="S4.T1.3.3.2">0.90</td> <td class="ltx_td ltx_align_center" id="S4.T1.3.3.3">27.33</td> </tr> </tbody> </table> <figcaption class="ltx_caption ltx_centering">Table 1: Kolmogorov-Smirnov statistic thresholds and corresponding contamination levels for different cutout sizes. The threshold was determined using only visually confirmed hostless objects with TNS classification and requiring completeness of 75%.</figcaption> </figure> </section> <section class="ltx_subsection" id="S4.SS2"> <h3 class="ltx_title ltx_title_subsection"> 4.2 Hostless sources on TNS</h3> <div class="ltx_para" id="S4.SS2.p1"> After applying the K-S <math alttext="D" class="ltx_Math" display="inline" id="S4.SS2.p1.1.m1.1"><semantics id="S4.SS2.p1.1.m1.1a"><mi id="S4.SS2.p1.1.m1.1.1" xref="S4.SS2.p1.1.m1.1.1.cmml">D</mi><annotation-xml encoding="MathML-Content" id="S4.SS2.p1.1.m1.1b"><ci id="S4.SS2.p1.1.m1.1.1.cmml" xref="S4.SS2.p1.1.m1.1.1">𝐷</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.SS2.p1.1.m1.1c">D</annotation><annotation encoding="application/x-llamapun" id="S4.SS2.p1.1.m1.1d">italic_D</annotation></semantics></math> statistic threshold to all the events flagged as hostless candidates by the image segmentation method, we find a total of 1563 ZTF events that match our criteria to be considered hostless candidates. We note that these events are flagged as hostless candidates because no extended source is found at the position of the transient at the center of the stamp. However, the transient could still be associated with a host that is either significantly off-center or that is dimmer than the limiting magnitude of the survey, which for ZTF is <math alttext="\sim" class="ltx_Math" display="inline" id="S4.SS2.p1.2.m2.1"><semantics id="S4.SS2.p1.2.m2.1a"><mo id="S4.SS2.p1.2.m2.1.1" xref="S4.SS2.p1.2.m2.1.1.cmml">∼</mo><annotation-xml encoding="MathML-Content" id="S4.SS2.p1.2.m2.1b"><csymbol cd="latexml" id="S4.SS2.p1.2.m2.1.1.cmml" xref="S4.SS2.p1.2.m2.1.1">similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S4.SS2.p1.2.m2.1c">\sim</annotation><annotation encoding="application/x-llamapun" id="S4.SS2.p1.2.m2.1d">∼</annotation></semantics></math> 20.5 mag <cite class="ltx_cite ltx_citemacro_citep">(Bellm et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib7" title="">2019</a>)</cite>. To define an event as truly hostless, user inspection is required. The retrieved number of hostless candidates represents <math alttext="\lesssim" class="ltx_Math" display="inline" id="S4.SS2.p1.3.m3.1"><semantics id="S4.SS2.p1.3.m3.1a"><mo id="S4.SS2.p1.3.m3.1.1" xref="S4.SS2.p1.3.m3.1.1.cmml">≲</mo><annotation-xml encoding="MathML-Content" id="S4.SS2.p1.3.m3.1b"><csymbol cd="latexml" id="S4.SS2.p1.3.m3.1.1.cmml" xref="S4.SS2.p1.3.m3.1.1">less-than-or-similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S4.SS2.p1.3.m3.1c">\lesssim</annotation><annotation encoding="application/x-llamapun" id="S4.SS2.p1.3.m3.1d">≲</annotation></semantics></math> 2% of the analyzed extragalactic transients and <math alttext="\lesssim" class="ltx_Math" display="inline" id="S4.SS2.p1.4.m4.1"><semantics id="S4.SS2.p1.4.m4.1a"><mo id="S4.SS2.p1.4.m4.1.1" xref="S4.SS2.p1.4.m4.1.1.cmml">≲</mo><annotation-xml encoding="MathML-Content" id="S4.SS2.p1.4.m4.1b"><csymbol cd="latexml" id="S4.SS2.p1.4.m4.1.1.cmml" xref="S4.SS2.p1.4.m4.1.1">less-than-or-similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S4.SS2.p1.4.m4.1c">\lesssim</annotation><annotation encoding="application/x-llamapun" id="S4.SS2.p1.4.m4.1d">≲</annotation></semantics></math> 0.01% of the number of transients processed by Fink between January/2022 and December/2023. </div> <div class="ltx_para" id="S4.SS2.p2"> Among the hostless candidates retrieved after applying the K-S statistic threshold (Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.SS1" title="4.1 𝐷 threshold for hostless candidates ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4.1</a>), 154 have an associated spectroscopic classification available on TNS. As the threshold was applied to the complete sample produced by the sigma clipping procedure (Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.SS2" title="3.2 Segmentation masks ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3.2</a>), including those events for which a host was spotted via visual inspection (see Section<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.SS1" title="4.1 𝐷 threshold for hostless candidates ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4.1</a>), 40 of the 154 hostless candidates with a TNS classification actually have a host that can be identified visually. In other words, the TNS classified hostless candidates present a <math alttext="\sim" class="ltx_Math" display="inline" id="S4.SS2.p2.1.m1.1"><semantics id="S4.SS2.p2.1.m1.1a"><mo id="S4.SS2.p2.1.m1.1.1" xref="S4.SS2.p2.1.m1.1.1.cmml">∼</mo><annotation-xml encoding="MathML-Content" id="S4.SS2.p2.1.m1.1b"><csymbol cd="latexml" id="S4.SS2.p2.1.m1.1.1.cmml" xref="S4.SS2.p2.1.m1.1.1">similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S4.SS2.p2.1.m1.1c">\sim</annotation><annotation encoding="application/x-llamapun" id="S4.SS2.p2.1.m1.1d">∼</annotation></semantics></math> 26% contamination, which is consistent with the value reported in Table <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.T1" title="Table 1 ‣ 4.1 𝐷 threshold for hostless candidates ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">1</a>. Table LABEL:tab:TNSsample-spec the 154 events together with the reported classification. We can see that the most common class is Type Ia SNe, encompassing <math alttext="\sim" class="ltx_Math" display="inline" id="S4.SS2.p2.2.m2.1"><semantics id="S4.SS2.p2.2.m2.1a"><mo id="S4.SS2.p2.2.m2.1.1" xref="S4.SS2.p2.2.m2.1.1.cmml">∼</mo><annotation-xml encoding="MathML-Content" id="S4.SS2.p2.2.m2.1b"><csymbol cd="latexml" id="S4.SS2.p2.2.m2.1.1.cmml" xref="S4.SS2.p2.2.m2.1.1">similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S4.SS2.p2.2.m2.1c">\sim</annotation><annotation encoding="application/x-llamapun" id="S4.SS2.p2.2.m2.1d">∼</annotation></semantics></math> 67.5% of events (considering all Type Ia subclasses). This is twice what was found by <cite class="ltx_cite ltx_citemacro_cite">McCrum et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib38" title="">2015</a>)</cite>, but it is consistent with SNe Ia being predominant among hostless transients. The second most common class is SLSNe, which encompasses <math alttext="\sim" class="ltx_Math" display="inline" id="S4.SS2.p2.3.m3.1"><semantics id="S4.SS2.p2.3.m3.1a"><mo id="S4.SS2.p2.3.m3.1.1" xref="S4.SS2.p2.3.m3.1.1.cmml">∼</mo><annotation-xml encoding="MathML-Content" id="S4.SS2.p2.3.m3.1b"><csymbol cd="latexml" id="S4.SS2.p2.3.m3.1.1.cmml" xref="S4.SS2.p2.3.m3.1.1">similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S4.SS2.p2.3.m3.1c">\sim</annotation><annotation encoding="application/x-llamapun" id="S4.SS2.p2.3.m3.1d">∼</annotation></semantics></math> 14% of the sample (considering both SLSNe I and SLSNe II). This is also consistent with the results of <cite class="ltx_cite ltx_citemacro_cite">McCrum et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib38" title="">2015</a>)</cite>. In a few cases, a transient reported to TNS is associated to more than one ZTF identifier, Table LABEL:tab:TNSsample-spec lists all of them, even if they are duplicated, this is because ELEPHANT only considers stamps associated to alerts, ignoring the associated coordinates. Inspecting the reasons for the duplicated ZTF identification is out of the scope of this paper. </div> <div class="ltx_para" id="S4.SS2.p3"> The last column of Table LABEL:tab:TNSsample-spec includes comments on some of the events. In particular, we see that a potential, usually faint, host has been reported on TNS for 11 events that we consider to be hostless. This is compatible with the contamination factor that we report above – further analysis is needed to confirm these associations. We also notice that eight of our hostless candidates were selected by the FLEET <cite class="ltx_cite ltx_citemacro_citep">(“Finding Luminous and Exotic Extragalactic Transients” Gomez et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib23" title="">2020</a>, <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib22" title="">2023</a>)</cite> pipeline as potentially luminous or exotic transients. In addition, five of our hostless candidates are part of the sample paper presented by <cite class="ltx_cite ltx_citemacro_cite">Chen et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib11" title="">2023</a>)</cite>, that analyzes the characteristics of 78 SLSNe I. Moreover, three of the SNe reported in Table LABEL:tab:TNSsample-spec were found in real-time by different groups, followed up, and studied in great detail due to their rare or anomalous nature. Below we provide further details on each of these events. </div> <figure class="ltx_figure" id="S4.F8"><img alt="Refer to caption" class="ltx_graphics ltx_img_landscape" height="503" id="S4.F8.g1" src="x11.png" width="829"/> <figcaption class="ltx_caption">Figure 8: Stacked template (left) and science (right) stamps for SLSN2018ibb (ZTF18acenqto, ZTF18adovhai).</figcaption> </figure> <figure class="ltx_figure" id="S4.F9"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="501" id="S4.F9.g1" src="x12.png" width="830"/> <figcaption class="ltx_caption ltx_centering">Figure 9: Stacked template (left) and science (right) stamps for SN2018bym (ZTF18aapgrxo).</figcaption> </figure> <figure class="ltx_figure" id="S4.F10"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="501" id="S4.F10.g1" src="x13.png" width="831"/> <figcaption class="ltx_caption ltx_centering">Figure 10: Stacked template (left) and science (right) stamps for SN2022ann (ZTF22aaaihet).</figcaption> </figure> <div class="ltx_para" id="S4.SS2.p4"> <ul class="ltx_itemize" id="S4.I1"> <li class="ltx_item" id="S4.I1.ix1" style="list-style-type:none;"> . <div class="ltx_para" id="S4.I1.ix1.p1"> SLSN 2018ibb was identified by <cite class="ltx_cite ltx_citemacro_cite">Schulze et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib46" title="">2024</a>)</cite> as the best pair-instability supernova (PISNe) candidate to date. It has been proposed that PISNe occur when instabilities produced by pair-production induce the thermonuclear explosion of the most massive stars (140 M<math alttext="{}_{\sun}<" class="ltx_math_unparsed" display="inline" id="S4.I1.ix1.p1.1.m1.1"><semantics id="S4.I1.ix1.p1.1.m1.1a"><mmultiscripts id="S4.I1.ix1.p1.1.m1.1.1"><mo id="S4.I1.ix1.p1.1.m1.1.1.2"><</mo><mprescripts id="S4.I1.ix1.p1.1.m1.1.1a"></mprescripts><mi id="S4.I1.ix1.p1.1.m1.1.1.3" mathvariant="normal">☉</mi><mrow id="S4.I1.ix1.p1.1.m1.1.1b"></mrow></mmultiscripts><annotation encoding="application/x-tex" id="S4.I1.ix1.p1.1.m1.1b">{}_{\sun}<</annotation><annotation encoding="application/x-llamapun" id="S4.I1.ix1.p1.1.m1.1c">start_FLOATSUBSCRIPT ☉ end_FLOATSUBSCRIPT <</annotation></semantics></math> M <math alttext="<" class="ltx_Math" display="inline" id="S4.I1.ix1.p1.2.m2.1"><semantics id="S4.I1.ix1.p1.2.m2.1a"><mo id="S4.I1.ix1.p1.2.m2.1.1" xref="S4.I1.ix1.p1.2.m2.1.1.cmml"><</mo><annotation-xml encoding="MathML-Content" id="S4.I1.ix1.p1.2.m2.1b"><lt id="S4.I1.ix1.p1.2.m2.1.1.cmml" xref="S4.I1.ix1.p1.2.m2.1.1"></lt></annotation-xml><annotation encoding="application/x-tex" id="S4.I1.ix1.p1.2.m2.1c"><</annotation><annotation encoding="application/x-llamapun" id="S4.I1.ix1.p1.2.m2.1d"><</annotation></semantics></math> 260 M☉). Thus, it has been proposed that PISNe mark the explosive death of Population III stars, which could be indirectly studied through the characteristics of the observed explosion <cite class="ltx_cite ltx_citemacro_citep">(e.g. Kasen et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib29" title="">2011</a>; Gal-Yam <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib18" title="">2012</a>)</cite>. Although SLSN 2018ibb is not hostless, it is associated with a faint <cite class="ltx_cite ltx_citemacro_citep">(m<math alttext="{}_{R}\sim" class="ltx_math_unparsed" display="inline" id="S4.I1.ix1.p1.4.1.m1.1"><semantics id="S4.I1.ix1.p1.4.1.m1.1a"><mmultiscripts id="S4.I1.ix1.p1.4.1.m1.1.1"><mo id="S4.I1.ix1.p1.4.1.m1.1.1.2">∼</mo><mprescripts id="S4.I1.ix1.p1.4.1.m1.1.1a"></mprescripts><mi id="S4.I1.ix1.p1.4.1.m1.1.1.3">R</mi><mrow id="S4.I1.ix1.p1.4.1.m1.1.1b"></mrow></mmultiscripts><annotation encoding="application/x-tex" id="S4.I1.ix1.p1.4.1.m1.1b">{}_{R}\sim</annotation><annotation encoding="application/x-llamapun" id="S4.I1.ix1.p1.4.1.m1.1c">start_FLOATSUBSCRIPT italic_R end_FLOATSUBSCRIPT ∼</annotation></semantics></math> 24.4 mag Schulze et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib46" title="">2024</a>)</cite> dwarf host, detected on 4- and 8-m class telescopes. Thus, for the purposes of the ZTF alerts processed by our pipeline, the transient is expected to appear hostless. Figure <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.F8" title="Figure 8 ‣ 4.2 Hostless sources on TNS ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">8</a> illustrates the interesting aspect which lead this object to be detected by our pipeline. It is a typical case of contaminated template, meaning that the template image was taken when the transient was bright, which results in a relatively lower central brightness in the science image. This result demonstrates the importance of considering both sets of stamps in parallel before a decision is made. </div> </li> <li class="ltx_item" id="S4.I1.ix2" style="list-style-type:none;"> . <div class="ltx_para" id="S4.I1.ix2.p1"> SN 2018bym was studied by <cite class="ltx_cite ltx_citemacro_cite">Lunnan et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib33" title="">2020</a>)</cite> alongside three other SLSNe discovered by ZTF to examine the origin and diversity of these events. The authors find that SN 2018bym can be considered a classical SLSN I, and that it is associated with a faint (m<math alttext="{}_{r}\sim" class="ltx_math_unparsed" display="inline" id="S4.I1.ix2.p1.1.m1.1"><semantics id="S4.I1.ix2.p1.1.m1.1a"><mmultiscripts id="S4.I1.ix2.p1.1.m1.1.1"><mo id="S4.I1.ix2.p1.1.m1.1.1.2">∼</mo><mprescripts id="S4.I1.ix2.p1.1.m1.1.1a"></mprescripts><mi id="S4.I1.ix2.p1.1.m1.1.1.3">r</mi><mrow id="S4.I1.ix2.p1.1.m1.1.1b"></mrow></mmultiscripts><annotation encoding="application/x-tex" id="S4.I1.ix2.p1.1.m1.1b">{}_{r}\sim</annotation><annotation encoding="application/x-llamapun" id="S4.I1.ix2.p1.1.m1.1c">start_FLOATSUBSCRIPT italic_r end_FLOATSUBSCRIPT ∼</annotation></semantics></math> 22.4 mag) dwarf galaxy, for which they obtained deeper observations with the Canada–France–Hawaii Telescope (CFHT). This event is also a representative case of template contamination, where the hostless stamp is the science one (Figure <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.F9" title="Figure 9 ‣ 4.2 Hostless sources on TNS ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">9</a>). </div> </li> <li class="ltx_item" id="S4.I1.ix3" style="list-style-type:none;"> . <div class="ltx_para" id="S4.I1.ix3.p1"> SN 2022ann was studied by <cite class="ltx_cite ltx_citemacro_cite">Davis et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib12" title="">2023</a>)</cite> as one of only five known SNe Icn. The early discovery of SN 2022ann enabled a detailed analysis of the progenitors of these rare objects. The authors find that SN 2022ann is associated with a faint dwarf host galaxy located in the lower end of the SN host galaxy luminosity distribution. Its stacked template and science stamps are shown in Figure <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.F10" title="Figure 10 ‣ 4.2 Hostless sources on TNS ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">10</a>. </div> </li> </ul> </div> <div class="ltx_para" id="S4.SS2.p5"> The fact that ELEPHANT was able to identify such interesting sources while analyzing historical data demonstrates its potential in identifying similarly interesting objects when applied to more recent alerts. We are currently working on such an investigation and, in parallel, integrating ELEPHANT to Fink. Preliminary results are encouraging and will be reported in a subsequent work. We also anticipate that, among other applications, the pipeline can serve as a powerful tool to identify SNe potentially associated to dwarf host galaxies <cite class="ltx_cite ltx_citemacro_citep">(e.g. Taggart & Perley <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib48" title="">2021</a>)</cite>. </div> <div class="ltx_para" id="S4.SS2.p6"> The classification distribution of the hostless candidates that do not have a class available on TNS is shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4.F11" title="Figure 11 ‣ 4.2 Hostless sources on TNS ‣ 4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">11</a>. The classification associated with these events is mainly obtained from cross-match with SIMBAD or inferred using a ML classifier. We find that <math alttext="\sim" class="ltx_Math" display="inline" id="S4.SS2.p6.1.m1.1"><semantics id="S4.SS2.p6.1.m1.1a"><mo id="S4.SS2.p6.1.m1.1.1" xref="S4.SS2.p6.1.m1.1.1.cmml">∼</mo><annotation-xml encoding="MathML-Content" id="S4.SS2.p6.1.m1.1b"><csymbol cd="latexml" id="S4.SS2.p6.1.m1.1.1.cmml" xref="S4.SS2.p6.1.m1.1.1">similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S4.SS2.p6.1.m1.1c">\sim</annotation><annotation encoding="application/x-llamapun" id="S4.SS2.p6.1.m1.1d">∼</annotation></semantics></math> 49% of these events are QSOs, which belong to the family of AGN and, thus, would be associated with a host by definition. However, hostless QSOs have been found before <cite class="ltx_cite ltx_citemacro_citep">(e.g. Magain et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib34" title="">2005</a>; Kemper et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib30" title="">2010</a>)</cite>. Although many of the QSOs in our sample of hostless candidates may be associated with a faint, undetected host, ELEPHANT can be used to perform systematic searches of hostless QSOs. The other dominant class in this sample is “SN candidate”, <math alttext="\sim" class="ltx_Math" display="inline" id="S4.SS2.p6.2.m2.1"><semantics id="S4.SS2.p6.2.m2.1a"><mo id="S4.SS2.p6.2.m2.1.1" xref="S4.SS2.p6.2.m2.1.1.cmml">∼</mo><annotation-xml encoding="MathML-Content" id="S4.SS2.p6.2.m2.1b"><csymbol cd="latexml" id="S4.SS2.p6.2.m2.1.1.cmml" xref="S4.SS2.p6.2.m2.1.1">similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S4.SS2.p6.2.m2.1c">\sim</annotation><annotation encoding="application/x-llamapun" id="S4.SS2.p6.2.m2.1d">∼</annotation></semantics></math> 48% of the sample is associated with this ML-based classification. As mentioned above, ELEPHANT only considers ZTF stamps associated to individual alerts, however, some events seems to be associated to multiple ZTF identifiers, when this occurs we considered all of the different identifications to be hostless candidates. An interesting case is that of AT 2024dum, this object was found to be a hostless candidate and is associated to three ZTF alerts: ZTF23aabtyzn, ZTF23aaiyhen and ZTF23abkiray. AT 2024dum has been reported to be a fast-moving star (see report101010<a class="ltx_ref ltx_url ltx_font_typewriter" href="https://www.wis-tns.org/object/2024dum" title="">https://www.wis-tns.org/object/2024dum</a> by Shumkov et al. 2024), which could explain the multiplicity of ZTF identifiers. </div> <figure class="ltx_figure" id="S4.F11"><img alt="Refer to caption" class="ltx_graphics ltx_img_square" height="830" id="S4.F11.g1" src="x14.png" width="830"/> <figcaption class="ltx_caption">Figure 11: Number of transients without a reported classification on TNS considered to be hostless by the sigma clipping method before applying the power spectrum (PS) analysis (orange), and the number of surviving hostless candidates after applying the PS analysis (blue).</figcaption> </figure> </section> </section> <section class="ltx_section" id="S5"> <h2 class="ltx_title ltx_title_section"> 5 Conclusions</h2> <div class="ltx_para" id="S5.p1"> We developed the ELEPHANT pipeline, which processes stamps delivered by the ZTF alert stream and automatically detects hostless transient candidates. The pipeline (see Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3" title="3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3</a>) returns stacked science and template cutouts together with the number of stamps that were used to produce them, a boolean that indicates whether the transient is a hostless candidate based on the segmentation mask analysis (see Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.SS2" title="3.2 Segmentation masks ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3.2</a>), the distance to the closest mask in pixels and the associated K-S <math alttext="D" class="ltx_Math" display="inline" id="S5.p1.1.m1.1"><semantics id="S5.p1.1.m1.1a"><mi id="S5.p1.1.m1.1.1" xref="S5.p1.1.m1.1.1.cmml">D</mi><annotation-xml encoding="MathML-Content" id="S5.p1.1.m1.1b"><ci id="S5.p1.1.m1.1.1.cmml" xref="S5.p1.1.m1.1.1">𝐷</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.p1.1.m1.1c">D</annotation><annotation encoding="application/x-llamapun" id="S5.p1.1.m1.1d">italic_D</annotation></semantics></math> statistic obtained from <math alttext="7\times 7" class="ltx_Math" display="inline" id="S5.p1.2.m2.1"><semantics id="S5.p1.2.m2.1a"><mrow id="S5.p1.2.m2.1.1" xref="S5.p1.2.m2.1.1.cmml"><mn id="S5.p1.2.m2.1.1.2" xref="S5.p1.2.m2.1.1.2.cmml">7</mn><mo id="S5.p1.2.m2.1.1.1" lspace="0.222em" rspace="0.222em" xref="S5.p1.2.m2.1.1.1.cmml">×</mo><mn id="S5.p1.2.m2.1.1.3" xref="S5.p1.2.m2.1.1.3.cmml">7</mn></mrow><annotation-xml encoding="MathML-Content" id="S5.p1.2.m2.1b"><apply id="S5.p1.2.m2.1.1.cmml" xref="S5.p1.2.m2.1.1"><times id="S5.p1.2.m2.1.1.1.cmml" xref="S5.p1.2.m2.1.1.1"></times><cn id="S5.p1.2.m2.1.1.2.cmml" type="integer" xref="S5.p1.2.m2.1.1.2">7</cn><cn id="S5.p1.2.m2.1.1.3.cmml" type="integer" xref="S5.p1.2.m2.1.1.3">7</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.p1.2.m2.1c">7\times 7</annotation><annotation encoding="application/x-llamapun" id="S5.p1.2.m2.1d">7 × 7</annotation></semantics></math>, <math alttext="15\times 15" class="ltx_Math" display="inline" id="S5.p1.3.m3.1"><semantics id="S5.p1.3.m3.1a"><mrow id="S5.p1.3.m3.1.1" xref="S5.p1.3.m3.1.1.cmml"><mn id="S5.p1.3.m3.1.1.2" xref="S5.p1.3.m3.1.1.2.cmml">15</mn><mo id="S5.p1.3.m3.1.1.1" lspace="0.222em" rspace="0.222em" xref="S5.p1.3.m3.1.1.1.cmml">×</mo><mn id="S5.p1.3.m3.1.1.3" xref="S5.p1.3.m3.1.1.3.cmml">15</mn></mrow><annotation-xml encoding="MathML-Content" id="S5.p1.3.m3.1b"><apply id="S5.p1.3.m3.1.1.cmml" xref="S5.p1.3.m3.1.1"><times id="S5.p1.3.m3.1.1.1.cmml" xref="S5.p1.3.m3.1.1.1"></times><cn id="S5.p1.3.m3.1.1.2.cmml" type="integer" xref="S5.p1.3.m3.1.1.2">15</cn><cn id="S5.p1.3.m3.1.1.3.cmml" type="integer" xref="S5.p1.3.m3.1.1.3">15</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.p1.3.m3.1c">15\times 15</annotation><annotation encoding="application/x-llamapun" id="S5.p1.3.m3.1d">15 × 15</annotation></semantics></math> and <math alttext="29\times 29" class="ltx_Math" display="inline" id="S5.p1.4.m4.1"><semantics id="S5.p1.4.m4.1a"><mrow id="S5.p1.4.m4.1.1" xref="S5.p1.4.m4.1.1.cmml"><mn id="S5.p1.4.m4.1.1.2" xref="S5.p1.4.m4.1.1.2.cmml">29</mn><mo id="S5.p1.4.m4.1.1.1" lspace="0.222em" rspace="0.222em" xref="S5.p1.4.m4.1.1.1.cmml">×</mo><mn id="S5.p1.4.m4.1.1.3" xref="S5.p1.4.m4.1.1.3.cmml">29</mn></mrow><annotation-xml encoding="MathML-Content" id="S5.p1.4.m4.1b"><apply id="S5.p1.4.m4.1.1.cmml" xref="S5.p1.4.m4.1.1"><times id="S5.p1.4.m4.1.1.1.cmml" xref="S5.p1.4.m4.1.1.1"></times><cn id="S5.p1.4.m4.1.1.2.cmml" type="integer" xref="S5.p1.4.m4.1.1.2">29</cn><cn id="S5.p1.4.m4.1.1.3.cmml" type="integer" xref="S5.p1.4.m4.1.1.3">29</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.p1.4.m4.1c">29\times 29</annotation><annotation encoding="application/x-llamapun" id="S5.p1.4.m4.1d">29 × 29</annotation></semantics></math> pixel square sub-cutouts (see Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S3.SS3" title="3.3 Host categorization via Fourier power spectrum ‣ 3 The ELEPHANT Pipeline ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">3.3</a>). </div> <div class="ltx_para" id="S5.p2"> In this work, we define a threshold on the K-S <math alttext="D" class="ltx_Math" display="inline" id="S5.p2.1.m1.1"><semantics id="S5.p2.1.m1.1a"><mi id="S5.p2.1.m1.1.1" xref="S5.p2.1.m1.1.1.cmml">D</mi><annotation-xml encoding="MathML-Content" id="S5.p2.1.m1.1b"><ci id="S5.p2.1.m1.1.1.cmml" xref="S5.p2.1.m1.1.1">𝐷</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.p2.1.m1.1c">D</annotation><annotation encoding="application/x-llamapun" id="S5.p2.1.m1.1d">italic_D</annotation></semantics></math> statistic that is used to flag a transient as a hostless candidate (see Section <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#S4" title="4 Results ‣ ELEPHANT: ExtragaLactic alErt Pipeline for Hostless AstroNomical Transients">4</a>). However, future users can use the output values to implement different selection cuts specific to their science case. The automatic detection of hostless transients has many potential applications that include but are not limited to: <ol class="ltx_enumerate" id="S5.I1"> <li class="ltx_item" id="S5.I1.i1" style="list-style-type:none;"> 1. <div class="ltx_para" id="S5.I1.i1.p1"> Identification of transients associated with dwarf and/or dim galaxies to study their characteristics and environments; </div> </li> <li class="ltx_item" id="S5.I1.i2" style="list-style-type:none;"> 2. <div class="ltx_para" id="S5.I1.i2.p1"> Identification of AGNs associated with low-mass galaxies to study their impact on galaxy evolution; </div> </li> <li class="ltx_item" id="S5.I1.i3" style="list-style-type:none;"> 3. <div class="ltx_para" id="S5.I1.i3.p1"> Search of sources that have been ejected from their host galaxies to study intra-cluster stellar populations; </div> </li> <li class="ltx_item" id="S5.I1.i4" style="list-style-type:none;"> 4. <div class="ltx_para" id="S5.I1.i4.p1"> Selection of SNe Ia and/or SLSNe, as they seem to be predominant among the hostless candidates that have a reported class on TNS; </div> </li> <li class="ltx_item" id="S5.I1.i5" style="list-style-type:none;"> 5. <div class="ltx_para" id="S5.I1.i5.p1"> Compilation of hostless candidates as training sets to improve ML classifiers. </div> </li> </ol> </div> <div class="ltx_para" id="S5.p3"> ELEPHANT will be included in the Fink broker to allow the real-time detection of hostless candidates and also the retrieval of archival potentially hostless events. Recently, <cite class="ltx_cite ltx_citemacro_cite">Qin et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib42" title="">2024</a>)</cite> performed an statistical analysis of the environments of 161 hostless SNe reported to TNS since 2016. They find that their sample is dominated by SNe Ia and SLSNe, which is in agreement with our findings. ELEPHANT is a useful tool to gather hostless events for similar statistical environmental analyses of different types of SNe. In addition, it can be used to systematically select hostless candidates for classification to increase the number of spectroscopically classified hostless transients to be considered in future population analyses. </div> <div class="ltx_para" id="S5.p4"> The methods we use here are completely transferable to any dataset by scaling the sizes of the considered stamps. In particular, once the Fink broker starts ingesting LSST alerts, we could test and tune ELEPHANT as a tool for finding hostless candidates within the LSST alert stream. LSST is an 8-m class telescope that will have a limiting magnitude of <math alttext="\sim" class="ltx_Math" display="inline" id="S5.p4.1.m1.1"><semantics id="S5.p4.1.m1.1a"><mo id="S5.p4.1.m1.1.1" xref="S5.p4.1.m1.1.1.cmml">∼</mo><annotation-xml encoding="MathML-Content" id="S5.p4.1.m1.1b"><csymbol cd="latexml" id="S5.p4.1.m1.1.1.cmml" xref="S5.p4.1.m1.1.1">similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S5.p4.1.m1.1c">\sim</annotation><annotation encoding="application/x-llamapun" id="S5.p4.1.m1.1d">∼</annotation></semantics></math>25 mag in optical bands <cite class="ltx_cite ltx_citemacro_citep">(LSST Science Collaboration et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib32" title="">2009</a>)</cite>, which makes it much deeper than the current wide-field surveys. Thus, a big fraction of the events that we flag as hostless candidates here may have a visible host in the LSST stamps. Consequently, if an LSST stamp is flagged to be a hostless by ELEPHANT the chances are that the transient is either part of the intra-cluster medium or, it is associated to hosts dimmer than any detected so far. We can only speculate that the hostless transients detected by LSST will be extraordinarily anomalous providing unprecedented insights to the transient sky, with the study of their environments only being possible by using other 8-m class telescopes or by the next generation of large telescopes such as the Giant Magellan Telescope <cite class="ltx_cite ltx_citemacro_citep">(Johns et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib27" title="">2012</a>)</cite> and the Extremely Large Telescope <cite class="ltx_cite ltx_citemacro_citep">(Gilmozzi & Spyromilio <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib21" title="">2007</a>)</cite>. In this context, automatic pipelines tailored for specific science cases, such as ELEPHANT will play a central role in the process of transient characterization and optimization of follow-up resources. {ThreePartTable} {TableNotes} </div> <div class="ltx_para" id="S5.p5"> First column presents the IAU name of each object. The second column shows the corresponding ZTF internal name. The third and fourth columns show right ascension and declination, respectively. Column five shows the classification available on TNS. In the sixth column we indicate whether we can visually confirm the lack of an obvious host associated with the transient. In the last column we add additional remarks about certain events. </div> <figure class="ltx_table" id="S5.T2"> <figcaption class="ltx_caption">Table 2: Hostless candidates with associated spectroscopic classification in TNS.</figcaption> <table class="ltx_tabular" id="S5.T2.41"> <thead class="ltx_thead"> <tr class="ltx_tr" id="S5.T2.41.42.1"> <th class="ltx_td ltx_nopad_l ltx_align_left ltx_th ltx_th_column" id="S5.T2.41.42.1.1" style="padding-left:2.0pt;padding-right:2.0pt;"> </th> <th class="ltx_td ltx_align_justify ltx_align_top ltx_th ltx_th_column" id="S5.T2.41.42.1.2" style="padding-left:2.0pt;padding-right:2.0pt;"></th> <th class="ltx_td ltx_align_justify ltx_align_top ltx_th ltx_th_column" id="S5.T2.41.42.1.3" style="padding-left:2.0pt;padding-right:2.0pt;"></th> <th class="ltx_td ltx_align_justify ltx_align_top ltx_th ltx_th_column" id="S5.T2.41.42.1.4" style="padding-left:2.0pt;padding-right:2.0pt;"></th> <th class="ltx_td ltx_th ltx_th_column" id="S5.T2.41.42.1.5" style="padding-left:2.0pt;padding-right:2.0pt;"></th> <th class="ltx_td ltx_th ltx_th_column" id="S5.T2.41.42.1.6" style="padding-left:2.0pt;padding-right:2.0pt;"></th> <th class="ltx_td ltx_align_justify ltx_align_top ltx_th ltx_th_column" id="S5.T2.41.42.1.7" style="padding-left:2.0pt;padding-right:2.0pt;"></th> </tr> </thead> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="S5.T2.41.43.1"> <td class="ltx_td ltx_nopad_l ltx_align_left ltx_border_tt" id="S5.T2.41.43.1.1" style="padding-left:2.0pt;padding-right:2.0pt;"> IAU Name</td> <td class="ltx_td ltx_align_justify ltx_align_top ltx_border_tt" id="S5.T2.41.43.1.2" style="padding-left:2.0pt;padding-right:2.0pt;"> ZTF Name </td> <td class="ltx_td ltx_align_justify ltx_align_top ltx_border_tt" id="S5.T2.41.43.1.3" style="padding-left:2.0pt;padding-right:2.0pt;"> R.A. </td> <td class="ltx_td ltx_align_justify ltx_align_top ltx_border_tt" id="S5.T2.41.43.1.4" style="padding-left:2.0pt;padding-right:2.0pt;"> Dec. </td> <td class="ltx_td ltx_align_left ltx_border_tt" id="S5.T2.41.43.1.5" style="padding-left:2.0pt;padding-right:2.0pt;">Class</td> <td class="ltx_td ltx_align_center ltx_border_tt" id="S5.T2.41.43.1.6" style="padding-left:2.0pt;padding-right:2.0pt;">Confirmed</td> <td class="ltx_td ltx_align_justify ltx_align_top ltx_border_tt" id="S5.T2.41.43.1.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Comments </td> </tr> <tr class="ltx_tr" id="S5.T2.41.44.2"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.44.2.1" style="padding-left:2.0pt;padding-right:2.0pt;"> </td> <td class="ltx_td ltx_align_top" id="S5.T2.41.44.2.2" style="padding-left:2.0pt;padding-right:2.0pt;"></td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.44.2.3" style="padding-left:2.0pt;padding-right:2.0pt;"> [J2000] </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.44.2.4" style="padding-left:2.0pt;padding-right:2.0pt;"> [J2000] </td> <td class="ltx_td" id="S5.T2.41.44.2.5" style="padding-left:2.0pt;padding-right:2.0pt;"></td> <td class="ltx_td" id="S5.T2.41.44.2.6" style="padding-left:2.0pt;padding-right:2.0pt;"></td> <td class="ltx_td ltx_align_top" id="S5.T2.41.44.2.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.1.1"> <td class="ltx_td ltx_nopad_l ltx_align_left ltx_border_t" id="S5.T2.1.1.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 1 SN 2016ieq</td> <td class="ltx_td ltx_align_justify ltx_align_top ltx_border_t" id="S5.T2.1.1.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF19abkaxlf" title="">ZTF19abkaxlf</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top ltx_border_t" id="S5.T2.1.1.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 21:22:25.18 </td> <td class="ltx_td ltx_align_justify ltx_align_top ltx_border_t" id="S5.T2.1.1.5" style="padding-left:2.0pt;padding-right:2.0pt;"> -11:56:54.82 </td> <td class="ltx_td ltx_align_left ltx_border_t" id="S5.T2.1.1.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIIn</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.1.1.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.1.1.1.m1.1"><semantics id="S5.T2.1.1.1.m1.1a"><mo id="S5.T2.1.1.1.m1.1.1" xref="S5.T2.1.1.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.1.1.1.m1.1b"><times id="S5.T2.1.1.1.m1.1.1.cmml" xref="S5.T2.1.1.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.1.1.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.1.1.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top ltx_border_t" id="S5.T2.1.1.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.45.3"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.45.3.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 2 SN 2017iuu</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.45.3.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aajwbhh" title="">ZTF18aajwbhh</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.45.3.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 06:27:40.06 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.45.3.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 47:29:45.51 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.45.3.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.45.3.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.45.3.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Several potential hosts, no redshift info. </td> </tr> <tr class="ltx_tr" id="S5.T2.2.2"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.2.2.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 3 SN 2018fd</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.2.2.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18adoeywv" title="">ZTF18adoeywv</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.2.2.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 09:10:36.36 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.2.2.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 35:43:18.39 </td> <td class="ltx_td ltx_align_left" id="S5.T2.2.2.6" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.2.2.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.2.2.1.m1.1"><semantics id="S5.T2.2.2.1.m1.1a"><mo id="S5.T2.2.2.1.m1.1.1" xref="S5.T2.2.2.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.2.2.1.m1.1b"><times id="S5.T2.2.2.1.m1.1.1.cmml" xref="S5.T2.2.2.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.2.2.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.2.2.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.2.2.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.3.3"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.3.3.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 4 SN 2018gj</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.3.3.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aaxljll" title="">ZTF18aaxljll</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.3.3.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 16:32:02.27 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.3.3.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 78:12:40.96 </td> <td class="ltx_td ltx_align_left" id="S5.T2.3.3.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNII</td> <td class="ltx_td ltx_align_center" id="S5.T2.3.3.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.3.3.1.m1.1"><semantics id="S5.T2.3.3.1.m1.1a"><mo id="S5.T2.3.3.1.m1.1.1" xref="S5.T2.3.3.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.3.3.1.m1.1b"><times id="S5.T2.3.3.1.m1.1.1.cmml" xref="S5.T2.3.3.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.3.3.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.3.3.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.3.3.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.4.4"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.4.4.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 5 SN 2018hh</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.4.4.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aaajfsd" title="">ZTF18aaajfsd</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.4.4.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 12:13:41.40 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.4.4.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 28:26:39.92 </td> <td class="ltx_td ltx_align_left" id="S5.T2.4.4.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.4.4.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.4.4.1.m1.1"><semantics id="S5.T2.4.4.1.m1.1a"><mo id="S5.T2.4.4.1.m1.1.1" xref="S5.T2.4.4.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.4.4.1.m1.1b"><times id="S5.T2.4.4.1.m1.1.1.cmml" xref="S5.T2.4.4.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.4.4.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.4.4.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.4.4.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.46.4"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.46.4.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 6 SN 2018kl</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.46.4.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aaacdnd" title="">ZTF18aaacdnd</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.46.4.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 09:09:37.99 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.46.4.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 48:39:39.95 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.46.4.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.46.4.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.46.4.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Potential host association on TNS. </td> </tr> <tr class="ltx_tr" id="S5.T2.5.5"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.5.5.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 7 SN 2018mc</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.5.5.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aatpnrf" title="">ZTF18aatpnrf</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.5.5.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 18:01:00.89 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.5.5.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 61:41:46.76 </td> <td class="ltx_td ltx_align_left" id="S5.T2.5.5.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIIb</td> <td class="ltx_td ltx_align_center" id="S5.T2.5.5.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.5.5.1.m1.1"><semantics id="S5.T2.5.5.1.m1.1a"><mo id="S5.T2.5.5.1.m1.1.1" xref="S5.T2.5.5.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.5.5.1.m1.1b"><times id="S5.T2.5.5.1.m1.1.1.cmml" xref="S5.T2.5.5.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.5.5.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.5.5.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.5.5.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.6.6"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.6.6.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 8 SN 2018vx</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.6.6.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18adkgxye" title="">ZTF18adkgxye</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.6.6.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 14:43:10.45 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.6.6.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 17:28:16.76 </td> <td class="ltx_td ltx_align_left" id="S5.T2.6.6.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa-91T-like</td> <td class="ltx_td ltx_align_center" id="S5.T2.6.6.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.6.6.1.m1.1"><semantics id="S5.T2.6.6.1.m1.1a"><mo id="S5.T2.6.6.1.m1.1.1" xref="S5.T2.6.6.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.6.6.1.m1.1b"><times id="S5.T2.6.6.1.m1.1.1.cmml" xref="S5.T2.6.6.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.6.6.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.6.6.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.6.6.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Potential host association on TNS. </td> </tr> <tr class="ltx_tr" id="S5.T2.7.7"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.7.7.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 9 SN 2018vx</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.7.7.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aaznlwl" title="">ZTF18aaznlwl</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.7.7.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 14:43:10.44 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.7.7.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 17:28:16.88 </td> <td class="ltx_td ltx_align_left" id="S5.T2.7.7.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa-91T-like</td> <td class="ltx_td ltx_align_center" id="S5.T2.7.7.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.7.7.1.m1.1"><semantics id="S5.T2.7.7.1.m1.1a"><mo id="S5.T2.7.7.1.m1.1.1" xref="S5.T2.7.7.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.7.7.1.m1.1b"><times id="S5.T2.7.7.1.m1.1.1.cmml" xref="S5.T2.7.7.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.7.7.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.7.7.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.7.7.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.8.8"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.8.8.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 10 SN 2018yc</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.8.8.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aabqgnb" title="">ZTF18aabqgnb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.8.8.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 11:52:45.48 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.8.8.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 37:51:15.44 </td> <td class="ltx_td ltx_align_left" id="S5.T2.8.8.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.8.8.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.8.8.1.m1.1"><semantics id="S5.T2.8.8.1.m1.1a"><mo id="S5.T2.8.8.1.m1.1.1" xref="S5.T2.8.8.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.8.8.1.m1.1b"><times id="S5.T2.8.8.1.m1.1.1.cmml" xref="S5.T2.8.8.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.8.8.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.8.8.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.8.8.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.47.5"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.47.5.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 11 SN 2018aae</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.47.5.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aaiscil" title="">ZTF18aaiscil</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.47.5.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 12:21:34.21 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.47.5.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 55:34:27.98 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.47.5.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.47.5.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.47.5.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Faint host in Gaia. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.48.6"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.48.6.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 12 SN 2018bym</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.48.6.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aapgrxo" title="">ZTF18aapgrxo</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.48.6.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 18:43:13.41 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.48.6.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 45:12:28.23 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.48.6.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.48.6.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.48.6.7" style="padding-left:2.0pt;padding-right:2.0pt;"> <cite class="ltx_cite ltx_citemacro_cite">Lunnan et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib33" title="">2020</a>); Chen et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib11" title="">2023</a>)</cite>. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.49.7"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.49.7.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 13 SN 2018cog</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.49.7.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aaxtcdm" title="">ZTF18aaxtcdm</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.49.7.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:26:11.95 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.49.7.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 06:21:25.87 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.49.7.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.49.7.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.49.7.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.9.9"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.9.9.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 14 SN 2018cxa</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.9.9.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18abfylqx" title="">ZTF18abfylqx</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.9.9.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 22:28:34.59 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.9.9.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 11:37:05.55 </td> <td class="ltx_td ltx_align_left" id="S5.T2.9.9.6" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.9.9.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.9.9.1.m1.1"><semantics id="S5.T2.9.9.1.m1.1a"><mo id="S5.T2.9.9.1.m1.1.1" xref="S5.T2.9.9.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.9.9.1.m1.1b"><times id="S5.T2.9.9.1.m1.1.1.cmml" xref="S5.T2.9.9.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.9.9.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.9.9.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.9.9.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.10.10"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.10.10.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 15 SN 2018eem</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.10.10.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18absoghh" title="">ZTF18absoghh</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.10.10.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 23:36:01.41 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.10.10.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 18:41:07.06 </td> <td class="ltx_td ltx_align_left" id="S5.T2.10.10.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNII</td> <td class="ltx_td ltx_align_center" id="S5.T2.10.10.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.10.10.1.m1.1"><semantics id="S5.T2.10.10.1.m1.1a"><mo id="S5.T2.10.10.1.m1.1.1" xref="S5.T2.10.10.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.10.10.1.m1.1b"><times id="S5.T2.10.10.1.m1.1.1.cmml" xref="S5.T2.10.10.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.10.10.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.10.10.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.10.10.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.11.11"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.11.11.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 16 SN 2018fcg</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.11.11.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18admasii" title="">ZTF18admasii</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.11.11.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 21:09:36.77 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.11.11.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 33:28:59.43 </td> <td class="ltx_td ltx_align_left" id="S5.T2.11.11.6" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.11.11.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.11.11.1.m1.1"><semantics id="S5.T2.11.11.1.m1.1a"><mo id="S5.T2.11.11.1.m1.1.1" xref="S5.T2.11.11.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.11.11.1.m1.1b"><times id="S5.T2.11.11.1.m1.1.1.cmml" xref="S5.T2.11.11.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.11.11.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.11.11.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.11.11.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.50.8"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.50.8.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 17 SN 2018fer</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.50.8.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18abtvstb" title="">ZTF18abtvstb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.50.8.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 20:33:05.24 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.50.8.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -20:51:24.43 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.50.8.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIIb</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.50.8.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.50.8.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.51.9"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.51.9.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 18 SN 2018ffj</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.51.9.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18abslpjy" title="">ZTF18abslpjy</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.51.9.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 02:30:59.80 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.51.9.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -17:20:26.84 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.51.9.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.51.9.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.51.9.7" style="padding-left:2.0pt;padding-right:2.0pt;"> <cite class="ltx_cite ltx_citemacro_cite">Garcia-Zamora et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib19" title="">2018</a>)</cite>. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.52.10"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.52.10.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 19 SN 2018ftd</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.52.10.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18abotdef" title="">ZTF18abotdef</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.52.10.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 02:01:16.09 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.52.10.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -01:13:26.91 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.52.10.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.52.10.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.52.10.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.12.12"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.12.12.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 20 SN 2018fus</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.12.12.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18abskoyh" title="">ZTF18abskoyh</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.12.12.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 21:02:31.29 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.12.12.5" style="padding-left:2.0pt;padding-right:2.0pt;"> -05:37:30.08 </td> <td class="ltx_td ltx_align_left" id="S5.T2.12.12.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNII</td> <td class="ltx_td ltx_align_center" id="S5.T2.12.12.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.12.12.1.m1.1"><semantics id="S5.T2.12.12.1.m1.1a"><mo id="S5.T2.12.12.1.m1.1.1" xref="S5.T2.12.12.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.12.12.1.m1.1b"><times id="S5.T2.12.12.1.m1.1.1.cmml" xref="S5.T2.12.12.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.12.12.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.12.12.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.12.12.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.53.11"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.53.11.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 21 SN 2018gck</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.53.11.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18abskzjm" title="">ZTF18abskzjm</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.53.11.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 00:50:56.6 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.53.11.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 03:29:55.20 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.53.11.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.53.11.6" rowspan="2" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.53.11.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.54.12"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.54.12.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 22 SN 2018gck</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.54.12.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18adnfkzf" title="">ZTF18adnfkzf</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.54.12.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 00:50:56.61 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.54.12.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 03:29:55.00 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.54.12.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.54.12.6" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.13.13"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.13.13.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 23 SN 2018gkz</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.13.13.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18abvgjyl" title="">ZTF18abvgjyl</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.13.13.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 07:58:11.55 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.13.13.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 19:31:07.99 </td> <td class="ltx_td ltx_align_left" id="S5.T2.13.13.6" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.13.13.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.13.13.1.m1.1"><semantics id="S5.T2.13.13.1.m1.1a"><mo id="S5.T2.13.13.1.m1.1.1" xref="S5.T2.13.13.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.13.13.1.m1.1b"><times id="S5.T2.13.13.1.m1.1.1.cmml" xref="S5.T2.13.13.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.13.13.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.13.13.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.13.13.7" style="padding-left:2.0pt;padding-right:2.0pt;"> <cite class="ltx_cite ltx_citemacro_cite">Chen et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib11" title="">2023</a>)</cite>. </td> </tr> <tr class="ltx_tr" id="S5.T2.14.14"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.14.14.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 24 SN 2018htb</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.14.14.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18acdqmxr" title="">ZTF18acdqmxr</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.14.14.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 04:37:30.67 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.14.14.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 20:16:55.70 </td> <td class="ltx_td ltx_align_left" id="S5.T2.14.14.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.14.14.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.14.14.1.m1.1"><semantics id="S5.T2.14.14.1.m1.1a"><mo id="S5.T2.14.14.1.m1.1.1" xref="S5.T2.14.14.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.14.14.1.m1.1b"><times id="S5.T2.14.14.1.m1.1.1.cmml" xref="S5.T2.14.14.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.14.14.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.14.14.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.14.14.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.55.13"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.55.13.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 25 SN 2018ibb</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.55.13.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18acenqto" title="">ZTF18acenqto</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.55.13.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 04:38:56.94 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.55.13.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -20:39:44.06 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.55.13.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.55.13.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.55.13.7" style="padding-left:2.0pt;padding-right:2.0pt;"> <cite class="ltx_cite ltx_citemacro_cite">Schulze et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib46" title="">2024</a>); Chen et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib11" title="">2023</a>)</cite>. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.56.14"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.56.14.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 26 SN 2018ibb</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.56.14.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18adovhai" title="">ZTF18adovhai</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.56.14.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 04:38:56.95 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.56.14.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -20:39:43.93 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.56.14.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.56.14.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.56.14.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.57.15"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.57.15.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 27 SN 2018icz</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.57.15.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18accngfb" title="">ZTF18accngfb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.57.15.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 10:03:14.82 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.57.15.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:04:42.87 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.57.15.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.57.15.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.57.15.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Gaia hostless candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.15.15"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.15.15.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 28 SN 2018imd</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.15.15.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18acydvjn" title="">ZTF18acydvjn</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.15.15.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 12:48:24.97 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.15.15.5" style="padding-left:2.0pt;padding-right:2.0pt;"> -05:47:39.10 </td> <td class="ltx_td ltx_align_left" id="S5.T2.15.15.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.15.15.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.15.15.1.m1.1"><semantics id="S5.T2.15.15.1.m1.1a"><mo id="S5.T2.15.15.1.m1.1.1" xref="S5.T2.15.15.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.15.15.1.m1.1b"><times id="S5.T2.15.15.1.m1.1.1.cmml" xref="S5.T2.15.15.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.15.15.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.15.15.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.15.15.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.58.16"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.58.16.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 29 SN 2018imq</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.58.16.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18acepwhb" title="">ZTF18acepwhb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.58.16.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 11:34:45.61 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.58.16.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 77:03:09.99 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.58.16.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.58.16.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.58.16.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.16.16"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.16.16.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 30 SN 2018jeo</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.16.16.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aczddnw" title="">ZTF18aczddnw</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.16.16.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 09:04:36.91 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.16.16.5" style="padding-left:2.0pt;padding-right:2.0pt;"> -19:47:09.60 </td> <td class="ltx_td ltx_align_left" id="S5.T2.16.16.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.16.16.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.16.16.1.m1.1"><semantics id="S5.T2.16.16.1.m1.1a"><mo id="S5.T2.16.16.1.m1.1.1" xref="S5.T2.16.16.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.16.16.1.m1.1b"><times id="S5.T2.16.16.1.m1.1.1.cmml" xref="S5.T2.16.16.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.16.16.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.16.16.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.16.16.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.59.17"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.59.17.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 31 SN 2018lzw</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.59.17.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18abrzcbp" title="">ZTF18abrzcbp</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.59.17.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 07:39:32.76 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.59.17.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 27:44:02.62 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.59.17.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.59.17.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.59.17.7" style="padding-left:2.0pt;padding-right:2.0pt;"> <cite class="ltx_cite ltx_citemacro_cite">Chen et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib11" title="">2023</a>)</cite>. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.60.18"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.60.18.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 32 SN 2018lzx</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.60.18.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18abszecm" title="">ZTF18abszecm</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.60.18.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 22:29:27.23 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.60.18.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:10:39.96 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.60.18.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.60.18.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.60.18.7" style="padding-left:2.0pt;padding-right:2.0pt;"> <cite class="ltx_cite ltx_citemacro_cite">Chen et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib11" title="">2023</a>)</cite>. </td> </tr> <tr class="ltx_tr" id="S5.T2.17.17"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.17.17.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 33 SN 2019aatt</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.17.17.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF19abszdld" title="">ZTF19abszdld</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.17.17.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 01:21:21.63 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.17.17.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 30:17:03.52 </td> <td class="ltx_td ltx_align_left" id="S5.T2.17.17.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.17.17.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.17.17.1.m1.1"><semantics id="S5.T2.17.17.1.m1.1a"><mo id="S5.T2.17.17.1.m1.1.1" xref="S5.T2.17.17.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.17.17.1.m1.1b"><times id="S5.T2.17.17.1.m1.1.1.cmml" xref="S5.T2.17.17.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.17.17.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.17.17.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.17.17.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.61.19"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.61.19.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 34 SN 2020jhs</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.61.19.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF20aayvmyh" title="">ZTF20aayvmyh</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.61.19.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 09:28:14.10 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.61.19.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 25:40:13.39 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.61.19.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIIn</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.61.19.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.61.19.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.62.20"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.62.20.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 35 SN 2021rll</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.62.20.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF21abiwpjm" title="">ZTF21abiwpjm</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.62.20.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:45:21.99 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.62.20.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 26:45:00.72 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.62.20.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIIn</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.62.20.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.62.20.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Faint host in Pan-STARRS. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.63.21"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.63.21.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 36 SN 2022aj</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.63.21.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaafohf" title="">ZTF22aaafohf</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.63.21.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 14:56:08.32 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.63.21.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -27:45:37.53 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.63.21.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.63.21.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.63.21.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Gaia hostless candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.64.22"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.64.22.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 37 SN 2022aj</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.64.22.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaausrb" title="">ZTF22aaausrb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.64.22.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 14:56:08.31 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.64.22.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -27:45:37.58 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.64.22.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.64.22.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.64.22.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Gaia hostless candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.65.23"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.65.23.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 38 SN 2022ait</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.65.23.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaaiykj" title="">ZTF22aaaiykj</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.65.23.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 10:30:26.97 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.65.23.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 07:10:21.19 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.65.23.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.65.23.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.65.23.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.66.24"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.66.24.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 39 SN 2022ann</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.66.24.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaaihet" title="">ZTF22aaaihet</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.66.24.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 10:17:29.66 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.66.24.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -02:25:35.40 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.66.24.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIcn</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.66.24.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.66.24.7" style="padding-left:2.0pt;padding-right:2.0pt;"> <cite class="ltx_cite ltx_citemacro_cite">Davis et al. (<a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib12" title="">2023</a>)</cite>. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.67.25"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.67.25.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 40 SN 2022are</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.67.25.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaahull" title="">ZTF22aaahull</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.67.25.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 09:59:07.08 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.67.25.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -18:11:02.83 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.67.25.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.67.25.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.67.25.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.68.26"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.68.26.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 41 SN 2022bic</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.68.26.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaagvyp" title="">ZTF22aaagvyp</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.68.26.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 08:39:08.93 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.68.26.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 60:59:16.25 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.68.26.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.68.26.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.68.26.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.69.27"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.69.27.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 42 SN 2022cjv</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.69.27.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaafavg" title="">ZTF22aaafavg</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.69.27.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 11:34:34.66 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.69.27.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 31:02:40.71 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.69.27.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.69.27.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.69.27.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.18.18"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.18.18.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 43 SN 2022ddh</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.18.18.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aabtyli" title="">ZTF22aabtyli</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.18.18.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 10:28:15.83 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.18.18.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 06:34:47.31 </td> <td class="ltx_td ltx_align_left" id="S5.T2.18.18.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.18.18.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.18.18.1.m1.1"><semantics id="S5.T2.18.18.1.m1.1a"><mo id="S5.T2.18.18.1.m1.1.1" xref="S5.T2.18.18.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.18.18.1.m1.1b"><times id="S5.T2.18.18.1.m1.1.1.cmml" xref="S5.T2.18.18.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.18.18.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.18.18.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.18.18.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.70.28"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.70.28.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 44 SN 2022dld</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.70.28.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aabwvot" title="">ZTF22aabwvot</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.70.28.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 14:06:16.60 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.70.28.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:29:30.89 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.70.28.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.70.28.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.70.28.7" style="padding-left:2.0pt;padding-right:2.0pt;"> FLEET Candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.71.29"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.71.29.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 45 SN 2022fjx</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.71.29.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aadlmgg" title="">ZTF22aadlmgg</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.71.29.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 10:43:30.16 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.71.29.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 19:04:58.70 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.71.29.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa-91bg-like</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.71.29.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.71.29.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.72.30"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.72.30.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 46 SN 2022ful</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.72.30.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aadeuwu" title="">ZTF22aadeuwu</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.72.30.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 19:20:10.68 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.72.30.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 50:23:42.41 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.72.30.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.72.30.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.72.30.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Gaia hostless candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.73.31"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.73.31.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 47 SN 2022ful</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.73.31.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aafumyr" title="">ZTF22aafumyr</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.73.31.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 19:20:10.67 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.73.31.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 50:23:42.40 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.73.31.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.73.31.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.73.31.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Gaia hostless candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.74.32"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.74.32.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 48 SN 2022gkv</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.74.32.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaftcmp" title="">ZTF22aaftcmp</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.74.32.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:57:51.12 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.74.32.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 29:55:10.78 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.74.32.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.74.32.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.74.32.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.75.33"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.75.33.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 49 SN 2022gkv</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.75.33.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aadetzs" title="">ZTF22aadetzs</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.75.33.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:57:51.12 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.75.33.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 29:55:10.82 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.75.33.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.75.33.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.75.33.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.19.19"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.19.19.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 50 SN 2022gsp</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.19.19.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aadqkgp" title="">ZTF22aadqkgp</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.19.19.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 14:53:08.28 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.19.19.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:59:57.53 </td> <td class="ltx_td ltx_align_left" id="S5.T2.19.19.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.19.19.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.19.19.1.m1.1"><semantics id="S5.T2.19.19.1.m1.1a"><mo id="S5.T2.19.19.1.m1.1.1" xref="S5.T2.19.19.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.19.19.1.m1.1b"><times id="S5.T2.19.19.1.m1.1.1.cmml" xref="S5.T2.19.19.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.19.19.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.19.19.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.19.19.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.76.34"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.76.34.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 51 SN 2022hdn</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.76.34.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aagbxrb" title="">ZTF22aagbxrb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.76.34.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:00:09.14 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.76.34.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 36:07:13.14 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.76.34.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIc-BL</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.76.34.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.76.34.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Potential host association on TNS. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.77.35"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.77.35.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 52 SN 2022huk</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.77.35.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aahaasc" title="">ZTF22aahaasc</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.77.35.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 10:14:12.85 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.77.35.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -23:41:17.10 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.77.35.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.77.35.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.77.35.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.20.20"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.20.20.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 53 SN 2022hwk</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.20.20.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aagzbux" title="">ZTF22aagzbux</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.20.20.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 12:45:59.22 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.20.20.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 59:15:37.04 </td> <td class="ltx_td ltx_align_left" id="S5.T2.20.20.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIIn</td> <td class="ltx_td ltx_align_center" id="S5.T2.20.20.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.20.20.1.m1.1"><semantics id="S5.T2.20.20.1.m1.1a"><mo id="S5.T2.20.20.1.m1.1.1" xref="S5.T2.20.20.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.20.20.1.m1.1b"><times id="S5.T2.20.20.1.m1.1.1.cmml" xref="S5.T2.20.20.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.20.20.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.20.20.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.20.20.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.78.36"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.78.36.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 54 SN 2022igq</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.78.36.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aahecwj" title="">ZTF22aahecwj</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.78.36.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:56:52.02 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.78.36.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 19:07:01.66 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.78.36.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.78.36.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.78.36.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.79.37"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.79.37.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 55 SN 2022ihz</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.79.37.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aahgxdt" title="">ZTF22aahgxdt</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.79.37.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 09:42:48.23 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.79.37.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -03:36:25.48 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.79.37.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa-91bg-like</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.79.37.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.79.37.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.80.38"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.80.38.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 56 SN 2022irt</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.80.38.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aahhubz" title="">ZTF22aahhubz</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.80.38.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 12:27:12.57 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.80.38.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 00:55:40.00 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.80.38.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.80.38.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.80.38.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.81.39"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.81.39.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 57 SN 2022jii</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.81.39.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaizxqg" title="">ZTF22aaizxqg</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.81.39.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 14:54:31.30 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.81.39.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 04:19:52.83 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.81.39.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.81.39.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.81.39.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Potential host association on TNS. </td> </tr> <tr class="ltx_tr" id="S5.T2.21.21"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.21.21.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 58 SN 2022jnr</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.21.21.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aajhtpy" title="">ZTF22aajhtpy</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.21.21.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:02:39.48 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.21.21.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 17:14:23.45 </td> <td class="ltx_td ltx_align_left" id="S5.T2.21.21.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.21.21.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.21.21.1.m1.1"><semantics id="S5.T2.21.21.1.m1.1a"><mo id="S5.T2.21.21.1.m1.1.1" xref="S5.T2.21.21.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.21.21.1.m1.1b"><times id="S5.T2.21.21.1.m1.1.1.cmml" xref="S5.T2.21.21.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.21.21.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.21.21.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.21.21.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.82.40"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.82.40.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 59 SN 2022jzt</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.82.40.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aakanzk" title="">ZTF22aakanzk</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.82.40.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:43:12.79 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.82.40.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 48:23:10.82 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.82.40.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.82.40.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.82.40.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Potential host association on TNS. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.83.41"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.83.41.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 60 SN 2022knm</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.83.41.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aakkmri" title="">ZTF22aakkmri</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.83.41.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:25:04.36 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.83.41.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -24:39:24.94 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.83.41.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.83.41.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.83.41.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.84.42"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.84.42.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 61 SN 2022llq</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.84.42.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aalmrqp" title="">ZTF22aalmrqp</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.84.42.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 12:03:16.55 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.84.42.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 51:49:54.24 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.84.42.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.84.42.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.84.42.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.85.43"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.85.43.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 62 SN 2022lxd</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.85.43.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaljlzq" title="">ZTF22aaljlzq</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.85.43.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 17:36:38.67 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.85.43.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 61:33:18.66 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.85.43.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.85.43.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.85.43.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.86.44"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.86.44.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 63 SN 2022mjk</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.86.44.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aapuake" title="">ZTF22aapuake</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.86.44.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 01:25:41.36 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.86.44.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 01:45:41.27 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.86.44.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.86.44.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.86.44.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.87.45"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.87.45.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 64 SN 2022nab</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.87.45.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaobrbd" title="">ZTF22aaobrbd</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.87.45.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 18:38:57.89 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.87.45.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 48:23:04.86 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.87.45.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.87.45.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.87.45.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.88.46"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.88.46.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 65 AT 2022nci</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.88.46.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaombjf" title="">ZTF22aaombjf</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.88.46.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 00:46:33.41 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.88.46.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 41:45:35.15 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.88.46.5" style="padding-left:2.0pt;padding-right:2.0pt;">Nova</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.88.46.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.88.46.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.89.47"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.89.47.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 66 SN 2022ncx</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.89.47.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaogwbd" title="">ZTF22aaogwbd</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.89.47.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 12:08:13.50 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.89.47.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 66:38:24.84 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.89.47.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa-91T-like</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.89.47.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.89.47.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.90.48"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.90.48.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 67 SN 2022ojm</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.90.48.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aapjqpn" title="">ZTF22aapjqpn</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.90.48.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 23:37:46.03 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.90.48.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 40:05:07.96 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.90.48.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.90.48.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.90.48.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.91.49"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.91.49.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 68 SN 2022orr</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.91.49.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aasaapb" title="">ZTF22aasaapb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.91.49.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:50:58.27 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.91.49.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 68:35:07.80 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.91.49.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.91.49.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.91.49.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.92.50"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.92.50.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 69 SN 2022owf</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.92.50.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aaszlph" title="">ZTF22aaszlph</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.92.50.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 23:26:09.97 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.92.50.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 27:42:02.97 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.92.50.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.92.50.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.92.50.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.22.22"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.22.22.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 70 SN 2022rfn</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.22.22.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abahblc" title="">ZTF22abahblc</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.22.22.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 19:11:28.98 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.22.22.5" style="padding-left:2.0pt;padding-right:2.0pt;"> -17:11:07.59 </td> <td class="ltx_td ltx_align_left" id="S5.T2.22.22.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.22.22.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.22.22.1.m1.1"><semantics id="S5.T2.22.22.1.m1.1a"><mo id="S5.T2.22.22.1.m1.1.1" xref="S5.T2.22.22.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.22.22.1.m1.1b"><times id="S5.T2.22.22.1.m1.1.1.cmml" xref="S5.T2.22.22.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.22.22.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.22.22.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.22.22.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.93.51"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.93.51.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 71 SN 2022rhl</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.93.51.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aasoali" title="">ZTF22aasoali</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.93.51.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 19:20:44.21 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.93.51.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 46:52:54.75 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.93.51.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIIn</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.93.51.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.93.51.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.94.52"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.94.52.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 72 SN 2022rpm</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.94.52.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abamxcl" title="">ZTF22abamxcl</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.94.52.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 02:01:11.36 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.94.52.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -05:51:59.41 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.94.52.5" style="padding-left:2.0pt;padding-right:2.0pt;">SN</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.94.52.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.94.52.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.23.23"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.23.23.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 73 SN 2022sff</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.23.23.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abdibiz" title="">ZTF22abdibiz</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.23.23.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 07:56:05.03 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.23.23.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 33:28:18.38 </td> <td class="ltx_td ltx_align_left" id="S5.T2.23.23.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.23.23.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.23.23.1.m1.1"><semantics id="S5.T2.23.23.1.m1.1a"><mo id="S5.T2.23.23.1.m1.1.1" xref="S5.T2.23.23.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.23.23.1.m1.1b"><times id="S5.T2.23.23.1.m1.1.1.cmml" xref="S5.T2.23.23.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.23.23.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.23.23.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.23.23.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.95.53"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.95.53.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 74 SN 2022tis</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.95.53.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abepfmn" title="">ZTF22abepfmn</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.95.53.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 21:10:35.86 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.95.53.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -09:30:14.39 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.95.53.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNII</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.95.53.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.95.53.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.96.54"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.96.54.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 75 SN 2022uhk</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.96.54.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abfwchw" title="">ZTF22abfwchw</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.96.54.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 18:50:17.25 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.96.54.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 75:27:59.88 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.96.54.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNII</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.96.54.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.96.54.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.97.55"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.97.55.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 76 SN 2022uot</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.97.55.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abfyvhf" title="">ZTF22abfyvhf</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.97.55.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 05:37:10.51 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.97.55.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 68:34:31.96 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.97.55.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIIn</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.97.55.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.97.55.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.98.56"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.98.56.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 77 SN 2022uwh</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.98.56.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abfxmvf" title="">ZTF22abfxmvf</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.98.56.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 23:53:37.16 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.98.56.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 11:22:58.08 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.98.56.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.98.56.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.98.56.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.99.57"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.99.57.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 78 SN 2022wlm</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.99.57.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abjafpr" title="">ZTF22abjafpr</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.99.57.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 05:56:46.63 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.99.57.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 48:06:20.85 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.99.57.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIc-BL</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.99.57.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.99.57.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.100.58"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.100.58.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 79 SN 2022wpp</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.100.58.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abjrpmv" title="">ZTF22abjrpmv</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.100.58.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 16:41:49.91 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.100.58.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:15:45.35 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.100.58.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.100.58.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.100.58.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.101.59"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.101.59.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 80 SN 2022wuw</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.101.59.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22ablcybb" title="">ZTF22ablcybb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.101.59.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 16:26:19.28 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.101.59.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 80:28:41.33 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.101.59.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.101.59.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.101.59.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.102.60"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.102.60.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 81 SN 2022wuy</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.102.60.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22ablhldn" title="">ZTF22ablhldn</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.102.60.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 06:44:23.34 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.102.60.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 32:14:53.21 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.102.60.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.102.60.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.102.60.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.103.61"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.103.61.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 82 SN 2022xjl</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.103.61.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abmpqbq" title="">ZTF22abmpqbq</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.103.61.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 23:57:11.78 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.103.61.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 05:36:17.35 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.103.61.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.103.61.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.103.61.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.104.62"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.104.62.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 83 SN 2022xxn</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.104.62.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abmxtqr" title="">ZTF22abmxtqr</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.104.62.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 01:18:56.59 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.104.62.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -12:57:44.93 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.104.62.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.104.62.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.104.62.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.24.24"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.24.24.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 84 SN 2022ycr</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.24.24.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abnwvyc" title="">ZTF22abnwvyc</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.24.24.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 21:23:27.18 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.24.24.5" style="padding-left:2.0pt;padding-right:2.0pt;"> -18:06:13.85 </td> <td class="ltx_td ltx_align_left" id="S5.T2.24.24.6" style="padding-left:2.0pt;padding-right:2.0pt;">Other</td> <td class="ltx_td ltx_align_center" id="S5.T2.24.24.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.24.24.1.m1.1"><semantics id="S5.T2.24.24.1.m1.1a"><mo id="S5.T2.24.24.1.m1.1.1" xref="S5.T2.24.24.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.24.24.1.m1.1b"><times id="S5.T2.24.24.1.m1.1.1.cmml" xref="S5.T2.24.24.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.24.24.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.24.24.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.24.24.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.105.63"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.105.63.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 85 SN 2022ydl</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.105.63.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abnqzle" title="">ZTF22abnqzle</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.105.63.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 22:40:04.43 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.105.63.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -06:38:28.35 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.105.63.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.105.63.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.105.63.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.25.25"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.25.25.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 86 SN 2022yig</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.25.25.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aboaiim" title="">ZTF22aboaiim</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.25.25.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 05:20:21.53 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.25.25.5" style="padding-left:2.0pt;padding-right:2.0pt;"> -20:54:41.61 </td> <td class="ltx_td ltx_align_left" id="S5.T2.25.25.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.25.25.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.25.25.1.m1.1"><semantics id="S5.T2.25.25.1.m1.1a"><mo id="S5.T2.25.25.1.m1.1.1" xref="S5.T2.25.25.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.25.25.1.m1.1b"><times id="S5.T2.25.25.1.m1.1.1.cmml" xref="S5.T2.25.25.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.25.25.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.25.25.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.25.25.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.26.26"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.26.26.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 87 SN 2022yru</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.26.26.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22aboixdd" title="">ZTF22aboixdd</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.26.26.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 10:27:28.41 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.26.26.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 70:59:02.23 </td> <td class="ltx_td ltx_align_left" id="S5.T2.26.26.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.26.26.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.26.26.1.m1.1"><semantics id="S5.T2.26.26.1.m1.1a"><mo id="S5.T2.26.26.1.m1.1.1" xref="S5.T2.26.26.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.26.26.1.m1.1b"><times id="S5.T2.26.26.1.m1.1.1.cmml" xref="S5.T2.26.26.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.26.26.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.26.26.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.26.26.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.27.27"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.27.27.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 88 AT 2022zzj</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.27.27.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abtltcw" title="">ZTF22abtltcw</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.27.27.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 00:41:25.73 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.27.27.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 40:44:23.34 </td> <td class="ltx_td ltx_align_left" id="S5.T2.27.27.6" style="padding-left:2.0pt;padding-right:2.0pt;">Nova</td> <td class="ltx_td ltx_align_center" id="S5.T2.27.27.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.27.27.1.m1.1"><semantics id="S5.T2.27.27.1.m1.1a"><mo id="S5.T2.27.27.1.m1.1.1" xref="S5.T2.27.27.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.27.27.1.m1.1b"><times id="S5.T2.27.27.1.m1.1.1.cmml" xref="S5.T2.27.27.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.27.27.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.27.27.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.27.27.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Potential host association on TNS. </td> </tr> <tr class="ltx_tr" id="S5.T2.28.28"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.28.28.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 89 SN 2022aahy</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.28.28.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abtsypf" title="">ZTF22abtsypf</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.28.28.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 06:58:56.24 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.28.28.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 39:38:06.90 </td> <td class="ltx_td ltx_align_left" id="S5.T2.28.28.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIIn</td> <td class="ltx_td ltx_align_center" id="S5.T2.28.28.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.28.28.1.m1.1"><semantics id="S5.T2.28.28.1.m1.1a"><mo id="S5.T2.28.28.1.m1.1.1" xref="S5.T2.28.28.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.28.28.1.m1.1b"><times id="S5.T2.28.28.1.m1.1.1.cmml" xref="S5.T2.28.28.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.28.28.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.28.28.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.28.28.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.106.64"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.106.64.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 90 SN 2022aahz</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.106.64.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abtotgu" title="">ZTF22abtotgu</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.106.64.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 12:25:54.64 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.106.64.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 06:45:02.96 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.106.64.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.106.64.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.106.64.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.107.65"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.107.65.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 91 SN 2022abtm</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.107.65.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abvngdr" title="">ZTF22abvngdr</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.107.65.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 23:03:54.16 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.107.65.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:46:19.84 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.107.65.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.107.65.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.107.65.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.29.29"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.29.29.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 92 SN 2022acfw</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.29.29.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abzakdd" title="">ZTF22abzakdd</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.29.29.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:21:06.78 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.29.29.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 27:54:53.79 </td> <td class="ltx_td ltx_align_left" id="S5.T2.29.29.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.29.29.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.29.29.1.m1.1"><semantics id="S5.T2.29.29.1.m1.1a"><mo id="S5.T2.29.29.1.m1.1.1" xref="S5.T2.29.29.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.29.29.1.m1.1b"><times id="S5.T2.29.29.1.m1.1.1.cmml" xref="S5.T2.29.29.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.29.29.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.29.29.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.29.29.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.108.66"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.108.66.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 93 SN 2022acmr</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.108.66.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abyhqkt" title="">ZTF22abyhqkt</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.108.66.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 02:02:39.45 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.108.66.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -07:02:22.67 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.108.66.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.108.66.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.108.66.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.109.67"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.109.67.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 94 SN 2022acsx</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.109.67.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abynkpz" title="">ZTF22abynkpz</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.109.67.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 06:12:59.10 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.109.67.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 68:48:45.39 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.109.67.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.109.67.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.109.67.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Faint host in DESI Legacy Surveys DR10. </td> </tr> <tr class="ltx_tr" id="S5.T2.30.30"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.30.30.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 95 SN 2022adbl</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.30.30.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abyuoan" title="">ZTF22abyuoan</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.30.30.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 07:57:29.24 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.30.30.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 62:25:39.25 </td> <td class="ltx_td ltx_align_left" id="S5.T2.30.30.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.30.30.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.30.30.1.m1.1"><semantics id="S5.T2.30.30.1.m1.1a"><mo id="S5.T2.30.30.1.m1.1.1" xref="S5.T2.30.30.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.30.30.1.m1.1b"><times id="S5.T2.30.30.1.m1.1.1.cmml" xref="S5.T2.30.30.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.30.30.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.30.30.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.30.30.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.110.68"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.110.68.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 96 SN 2022adrs</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.110.68.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abzbyyw" title="">ZTF22abzbyyw</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.110.68.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 00:27:08.37 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.110.68.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -24:53:50.88 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.110.68.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.110.68.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.110.68.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.111.69"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.111.69.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 97 SN 2022advb</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.111.69.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abyznto" title="">ZTF22abyznto</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.111.69.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 09:40:44.48 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.111.69.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 05:10:21.13 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.111.69.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.111.69.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.111.69.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.112.70"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.112.70.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 98 SN 2022adxq</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.112.70.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abzvyku" title="">ZTF22abzvyku</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.112.70.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 03:27:24.99 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.112.70.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -17:37:50.35 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.112.70.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.112.70.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.112.70.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.31.31"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.31.31.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 99 SN 2023ha</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.31.31.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaajtqn" title="">ZTF23aaajtqn</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.31.31.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 09:19:32.46 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.31.31.5" style="padding-left:2.0pt;padding-right:2.0pt;"> -01:11:34.62 </td> <td class="ltx_td ltx_align_left" id="S5.T2.31.31.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.31.31.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.31.31.1.m1.1"><semantics id="S5.T2.31.31.1.m1.1a"><mo id="S5.T2.31.31.1.m1.1.1" xref="S5.T2.31.31.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.31.31.1.m1.1b"><times id="S5.T2.31.31.1.m1.1.1.cmml" xref="S5.T2.31.31.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.31.31.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.31.31.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.31.31.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.113.71"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.113.71.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 100 SN 2023ael</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.113.71.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaawbsy" title="">ZTF23aaawbsy</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.113.71.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 17:14:41.46 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.113.71.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 66:51:22.60 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.113.71.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.113.71.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.113.71.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Gaia hostless candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.32.32"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.32.32.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 101 SN 2023aiw</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.32.32.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaawcvx" title="">ZTF23aaawcvx</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.32.32.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 16:31:09.06 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.32.32.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 39:47:20.59 </td> <td class="ltx_td ltx_align_left" id="S5.T2.32.32.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.32.32.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.32.32.1.m1.1"><semantics id="S5.T2.32.32.1.m1.1a"><mo id="S5.T2.32.32.1.m1.1.1" xref="S5.T2.32.32.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.32.32.1.m1.1b"><times id="S5.T2.32.32.1.m1.1.1.cmml" xref="S5.T2.32.32.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.32.32.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.32.32.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.32.32.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.114.72"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.114.72.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 102 SN 2023ayq</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.114.72.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaazegi" title="">ZTF23aaazegi</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.114.72.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:24:05.23 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.114.72.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -03:33:41.04 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.114.72.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa-CSM</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.114.72.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.114.72.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.33.33"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.33.33.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 103 SN 2023bee</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.33.33.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aabtgej" title="">ZTF23aabtgej</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.33.33.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 08:56:11.63 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.33.33.5" style="padding-left:2.0pt;padding-right:2.0pt;"> -03:19:32.05 </td> <td class="ltx_td ltx_align_left" id="S5.T2.33.33.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.33.33.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.33.33.1.m1.1"><semantics id="S5.T2.33.33.1.m1.1a"><mo id="S5.T2.33.33.1.m1.1.1" xref="S5.T2.33.33.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.33.33.1.m1.1b"><times id="S5.T2.33.33.1.m1.1.1.cmml" xref="S5.T2.33.33.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.33.33.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.33.33.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.33.33.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.115.73"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.115.73.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 104 SN 2023cpq</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.115.73.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aacdnjz" title="">ZTF23aacdnjz</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.115.73.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 17:29:20.16 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.115.73.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 14:11:04.51 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.115.73.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa-CSM</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.115.73.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.115.73.7" style="padding-left:2.0pt;padding-right:2.0pt;"> FLEET Candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.116.74"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.116.74.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 105 SN 2023cze</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.116.74.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aadbswn" title="">ZTF23aadbswn</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.116.74.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:05:05.39 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.116.74.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 28:28:52.45 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.116.74.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.116.74.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.116.74.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.117.75"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.117.75.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 106 SN 2023ebb</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.117.75.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aadruma" title="">ZTF23aadruma</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.117.75.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 11:24:34.69 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.117.75.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 46:53:37.14 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.117.75.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNII</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.117.75.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.117.75.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.34.34"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.34.34.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 107 SN 2023erb</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.34.34.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaejvzv" title="">ZTF23aaejvzv</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.34.34.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 16:37:54.80 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.34.34.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 43:23:08.60 </td> <td class="ltx_td ltx_align_left" id="S5.T2.34.34.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.34.34.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.34.34.1.m1.1"><semantics id="S5.T2.34.34.1.m1.1a"><mo id="S5.T2.34.34.1.m1.1.1" xref="S5.T2.34.34.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.34.34.1.m1.1b"><times id="S5.T2.34.34.1.m1.1.1.cmml" xref="S5.T2.34.34.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.34.34.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.34.34.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.34.34.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.118.76"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.118.76.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 108 SN 2023exi</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.118.76.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaelzdb" title="">ZTF23aaelzdb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.118.76.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 07:04:14.64 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.118.76.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 67:37:32.53 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.118.76.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.118.76.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.118.76.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.119.77"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.119.77.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 109 SN 2023ffw</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.119.77.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaemgto" title="">ZTF23aaemgto</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.119.77.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 11:35:12.53 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.119.77.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -13:30:47.90 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.119.77.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.119.77.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.119.77.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.35.35"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.35.35.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 110 SN 2023fvf</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.35.35.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aafggjj" title="">ZTF23aafggjj</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.35.35.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:20:51.42 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.35.35.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:17:37.91 </td> <td class="ltx_td ltx_align_left" id="S5.T2.35.35.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.35.35.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.35.35.1.m1.1"><semantics id="S5.T2.35.35.1.m1.1a"><mo id="S5.T2.35.35.1.m1.1.1" xref="S5.T2.35.35.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.35.35.1.m1.1b"><times id="S5.T2.35.35.1.m1.1.1.cmml" xref="S5.T2.35.35.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.35.35.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.35.35.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.35.35.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.120.78"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.120.78.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 111 SN 2023gav</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.120.78.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaftouh" title="">ZTF23aaftouh</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.120.78.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 10:47:18.35 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.120.78.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -05:07:22.75 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.120.78.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.120.78.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.120.78.7" style="padding-left:2.0pt;padding-right:2.0pt;"> FLEET Candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.121.79"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.121.79.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 112 SN 2023ger</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.121.79.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aagaiju" title="">ZTF23aagaiju</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.121.79.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 10:57:13.46 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.121.79.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 42:58:50.06 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.121.79.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.121.79.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.121.79.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.122.80"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.122.80.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 113 SN 2023ghq</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.122.80.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aagunkc" title="">ZTF23aagunkc</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.122.80.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:58:13.05 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.122.80.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 08:54:24.99 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.122.80.5" style="padding-left:2.0pt;padding-right:2.0pt;">Other</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.122.80.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.122.80.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.123.81"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.123.81.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 114 SN 2023hoz</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.123.81.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aagdbbv" title="">ZTF23aagdbbv</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.123.81.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 16:18:21.55 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.123.81.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 01:31:43.41 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.123.81.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.123.81.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.123.81.7" style="padding-left:2.0pt;padding-right:2.0pt;"> FLEET Candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.36.36"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.36.36.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 115 SN 2023hrn</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.36.36.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaiyexs" title="">ZTF23aaiyexs</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.36.36.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 11:08:35.07 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.36.36.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 04:48:52.09 </td> <td class="ltx_td ltx_align_left" id="S5.T2.36.36.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.36.36.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.36.36.1.m1.1"><semantics id="S5.T2.36.36.1.m1.1a"><mo id="S5.T2.36.36.1.m1.1.1" xref="S5.T2.36.36.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.36.36.1.m1.1b"><times id="S5.T2.36.36.1.m1.1.1.cmml" xref="S5.T2.36.36.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.36.36.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.36.36.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.36.36.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.124.82"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.124.82.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 116 SN 2023huv</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.124.82.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aafmjbx" title="">ZTF23aafmjbx</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.124.82.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:29:03.66 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.124.82.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -10:25:29.42 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.124.82.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIIn</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.124.82.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.124.82.7" style="padding-left:2.0pt;padding-right:2.0pt;"> FLEET Candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.125.83"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.125.83.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 117 SN 2023iar</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.125.83.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aajenxf" title="">ZTF23aajenxf</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.125.83.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:31:36.14 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.125.83.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 04:55:21.32 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.125.83.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.125.83.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.125.83.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.37.37"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.37.37.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 118 SN 2023ifa</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.37.37.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aajhtuu" title="">ZTF23aajhtuu</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.37.37.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 09:33:34.73 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.37.37.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 51:36:54.11 </td> <td class="ltx_td ltx_align_left" id="S5.T2.37.37.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIbn</td> <td class="ltx_td ltx_align_center" id="S5.T2.37.37.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.37.37.1.m1.1"><semantics id="S5.T2.37.37.1.m1.1a"><mo id="S5.T2.37.37.1.m1.1.1" xref="S5.T2.37.37.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.37.37.1.m1.1b"><times id="S5.T2.37.37.1.m1.1.1.cmml" xref="S5.T2.37.37.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.37.37.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.37.37.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.37.37.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.126.84"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.126.84.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 119 SN 2023iwy</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.126.84.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aakmewi" title="">ZTF23aakmewi</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.126.84.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 18:00:18.62 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.126.84.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 26:24:32.04 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.126.84.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIc-BL</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.126.84.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.126.84.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.127.85"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.127.85.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 120 SN 2023jsb</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.127.85.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aamfmqm" title="">ZTF23aamfmqm</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.127.85.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 21:49:58.44 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.127.85.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 14:09:24.71 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.127.85.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.127.85.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.127.85.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.38.38"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.38.38.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 121 SN 2023jvu</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.38.38.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aamqonh" title="">ZTF23aamqonh</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.38.38.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 16:38:00.64 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.38.38.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 55:24:18.30 </td> <td class="ltx_td ltx_align_left" id="S5.T2.38.38.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.38.38.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.38.38.1.m1.1"><semantics id="S5.T2.38.38.1.m1.1a"><mo id="S5.T2.38.38.1.m1.1.1" xref="S5.T2.38.38.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.38.38.1.m1.1b"><times id="S5.T2.38.38.1.m1.1.1.cmml" xref="S5.T2.38.38.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.38.38.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.38.38.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.38.38.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.128.86"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.128.86.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 122 SN 2023khp</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.128.86.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aamsekn" title="">ZTF23aamsekn</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.128.86.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 00:17:56.20 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.128.86.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 23:59:03.33 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.128.86.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa-CSM</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.128.86.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.128.86.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.129.87"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.129.87.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 123 SN 2023kkh</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.129.87.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aanuvih" title="">ZTF23aanuvih</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.129.87.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 18:49:05.23 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.129.87.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 45:07:10.91 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.129.87.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.129.87.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.129.87.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.130.88"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.130.88.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 124 SN 2023kki</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.130.88.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aamxeoe" title="">ZTF23aamxeoe</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.130.88.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 16:53:18.11 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.130.88.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 37:41:23.52 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.130.88.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIIn</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.130.88.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.130.88.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.131.89"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.131.89.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 125 SN 2023kvk</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.131.89.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aanukvi" title="">ZTF23aanukvi</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.131.89.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 20:02:32.44 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.131.89.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -05:05:16.88 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.131.89.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.131.89.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.131.89.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.132.90"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.132.90.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 126 SN 2023mhj</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.132.90.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aapvrkk" title="">ZTF23aapvrkk</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.132.90.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 00:00:42.10 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.132.90.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -12:14:12.51 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.132.90.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.132.90.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.132.90.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.133.91"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.133.91.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 127 SN 2023mir</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.133.91.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaqfdby" title="">ZTF23aaqfdby</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.133.91.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 22:40:59.46 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.133.91.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -05:04:15.74 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.133.91.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.133.91.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.133.91.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.134.92"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.134.92.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 128 SN 2023mit</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.134.92.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaqjuux" title="">ZTF23aaqjuux</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.134.92.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 16:28:18.62 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.134.92.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 23:10:56.15 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.134.92.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.134.92.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.134.92.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.39.39"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.39.39.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 129 SN 2023nbf</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.39.39.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aawcygl" title="">ZTF23aawcygl</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.39.39.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 13:08:46.93 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.39.39.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 49:24:08.67 </td> <td class="ltx_td ltx_align_left" id="S5.T2.39.39.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.39.39.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.39.39.1.m1.1"><semantics id="S5.T2.39.39.1.m1.1a"><mo id="S5.T2.39.39.1.m1.1.1" xref="S5.T2.39.39.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.39.39.1.m1.1b"><times id="S5.T2.39.39.1.m1.1.1.cmml" xref="S5.T2.39.39.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.39.39.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.39.39.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.39.39.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.135.93"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.135.93.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 130 SN 2023pjx</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.135.93.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaxyawz" title="">ZTF23aaxyawz</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.135.93.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 01:31:25.59 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.135.93.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 12:24:31.35 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.135.93.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.135.93.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.135.93.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.136.94"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.136.94.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 131 SN 2023qpe</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.136.94.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aazrtdy" title="">ZTF23aazrtdy</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.136.94.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 23:40:15.79 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.136.94.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:27:50.97 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.136.94.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.136.94.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.136.94.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Potential host association on TNS. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.137.95"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.137.95.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 132 SN 2023qrz</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.137.95.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaznifc" title="">ZTF23aaznifc</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.137.95.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 21:55:14.72 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.137.95.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -17:35:31.55 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.137.95.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.137.95.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.137.95.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.138.96"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.138.96.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 133 SN 2023qvl</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.138.96.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aawhcjb" title="">ZTF23aawhcjb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.138.96.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 15:50:08.30 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.138.96.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 53:39:37.03 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.138.96.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.138.96.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.138.96.7" style="padding-left:2.0pt;padding-right:2.0pt;"> FLEET Candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.40.40"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.40.40.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 134 SN 2023qzo</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.40.40.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abaderr" title="">ZTF23abaderr</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.40.40.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 01:35:05.20 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.40.40.5" style="padding-left:2.0pt;padding-right:2.0pt;"> -22:40:37.84 </td> <td class="ltx_td ltx_align_left" id="S5.T2.40.40.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.40.40.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.40.40.1.m1.1"><semantics id="S5.T2.40.40.1.m1.1a"><mo id="S5.T2.40.40.1.m1.1.1" xref="S5.T2.40.40.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.40.40.1.m1.1b"><times id="S5.T2.40.40.1.m1.1.1.cmml" xref="S5.T2.40.40.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.40.40.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.40.40.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.40.40.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.139.97"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.139.97.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 135 SN 2023rbt</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.139.97.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abaslfm" title="">ZTF23abaslfm</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.139.97.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 01:46:31.43 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.139.97.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 11:51:55.34 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.139.97.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.139.97.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.139.97.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.140.98"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.140.98.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 136 SN 2023rfg</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.140.98.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abavpyk" title="">ZTF23abavpyk</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.140.98.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 23:31:06.17 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.140.98.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -27:00:56.44 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.140.98.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.140.98.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.140.98.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.141.99"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.141.99.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 137 SN 2023slt</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.141.99.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abbsfxp" title="">ZTF23abbsfxp</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.141.99.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 03:34:04.42 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.141.99.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -21:54:21.92 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.141.99.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.141.99.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.141.99.7" style="padding-left:2.0pt;padding-right:2.0pt;"> FLEET candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.142.100"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.142.100.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 138 SN 2023spg</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.142.100.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abcufxh" title="">ZTF23abcufxh</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.142.100.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 00:11:56.30 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.142.100.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -07:46:19.56 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.142.100.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.142.100.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.142.100.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.143.101"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.143.101.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 139 SN 2023svf</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.143.101.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abcqzvm" title="">ZTF23abcqzvm</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.143.101.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 16:44:05.26 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.143.101.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 30:18:09.99 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.143.101.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.143.101.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.143.101.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.144.102"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.144.102.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 140 SN 2023syg</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.144.102.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abdynfn" title="">ZTF23abdynfn</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.144.102.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 20:49:40.99 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.144.102.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -14:43:26.57 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.144.102.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.144.102.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.144.102.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.145.103"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.145.103.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 141 SN 2023szi</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.145.103.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aaznlgb" title="">ZTF23aaznlgb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.145.103.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 22:19:56.03 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.145.103.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 25:54:56.17 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.145.103.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.145.103.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.145.103.7" style="padding-left:2.0pt;padding-right:2.0pt;"> FLEET Candidate. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.146.104"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.146.104.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 142 SN 2023tqm</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.146.104.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abgvtxr" title="">ZTF23abgvtxr</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.146.104.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 07:57:28.61 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.146.104.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 51:07:23.93 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.146.104.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.146.104.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.146.104.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.147.105"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.147.105.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 143 SN 2023upt</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.147.105.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abjqxbe" title="">ZTF23abjqxbe</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.147.105.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 04:28:27.38 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.147.105.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -17:53:27.26 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.147.105.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.147.105.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.147.105.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.148.106"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.148.106.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 144 SN 2023uqu</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.148.106.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abijopy" title="">ZTF23abijopy</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.148.106.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 17:47:47.83 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.148.106.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 64:20:57.31 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.148.106.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.148.106.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.148.106.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Potential host association on TNS. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.149.107"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.149.107.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 145 SN 2023vkz</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.149.107.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23ablspnz" title="">ZTF23ablspnz</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.149.107.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 08:28:36.18 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.149.107.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 57:12:31.86 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.149.107.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNII</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.149.107.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.149.107.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.150.108"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.150.108.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 146 SN 2023wml</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.150.108.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aboebgh" title="">ZTF23aboebgh</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.150.108.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 11:39:08.69 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.150.108.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -11:14:57.92 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.150.108.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-I</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.150.108.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.150.108.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.151.109"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.151.109.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 147 SN 2023wrn</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.151.109.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23aboemfi" title="">ZTF23aboemfi</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.151.109.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 23:31:53.52 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.151.109.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 22:39:30.74 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.151.109.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.151.109.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.151.109.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.152.110"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.152.110.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 148 SN 2023wtq</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.152.110.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abochfb" title="">ZTF23abochfb</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.152.110.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 01:21:55.68 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.152.110.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -03:46:19.95 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.152.110.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIc-BL</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.152.110.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.152.110.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.153.111"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.153.111.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 149 SN 2023xjs</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.153.111.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abpqklj" title="">ZTF23abpqklj</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.153.111.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 02:26:34.56 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.153.111.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -19:10:26.42 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.153.111.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.153.111.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.153.111.7" style="padding-left:2.0pt;padding-right:2.0pt;"> Faint host in Pan-STARRS. </td> </tr> <tr class="ltx_tr" id="S5.T2.41.154.112"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.154.112.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 150 SN 2023yqq</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.154.112.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abryfga" title="">ZTF23abryfga</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.154.112.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 22:56:04.96 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.154.112.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 19:34:56.71 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.154.112.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.154.112.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.154.112.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.155.113"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.155.113.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 151 SN 2023yti</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.155.113.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23absflyh" title="">ZTF23absflyh</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.155.113.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 02:06:22.20 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.155.113.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -18:19:06.12 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.155.113.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.155.113.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.155.113.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.156.114"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.156.114.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 152 SN 2023zeq</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.156.114.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abqygjv" title="">ZTF23abqygjv</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.156.114.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 01:08:54.20 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.156.114.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -20:38:24.23 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.156.114.5" style="padding-left:2.0pt;padding-right:2.0pt;">SLSN-II</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.156.114.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.156.114.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.41"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.41.2" style="padding-left:2.0pt;padding-right:2.0pt;"> 153 SN 2023zjv</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.41.3" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23absbyol" title="">ZTF23absbyol</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.41.4" style="padding-left:2.0pt;padding-right:2.0pt;"> 07:14:10.46 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.41.5" style="padding-left:2.0pt;padding-right:2.0pt;"> 36:09:52.82 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.41.6" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.41.1" style="padding-left:2.0pt;padding-right:2.0pt;"><math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.41.41.1.m1.1"><semantics id="S5.T2.41.41.1.m1.1a"><mo id="S5.T2.41.41.1.m1.1.1" xref="S5.T2.41.41.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.41.41.1.m1.1b"><times id="S5.T2.41.41.1.m1.1.1.cmml" xref="S5.T2.41.41.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.41.41.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.41.41.1.m1.1d">×</annotation></semantics></math></td> <td class="ltx_td ltx_align_top" id="S5.T2.41.41.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.157.115"> <td class="ltx_td ltx_nopad_l ltx_align_left" id="S5.T2.41.157.115.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 154 SN 2023aajn</td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.157.115.2" style="padding-left:2.0pt;padding-right:2.0pt;"> <a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abvbwys" title="">ZTF23abvbwys</a> </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.157.115.3" style="padding-left:2.0pt;padding-right:2.0pt;"> 03:41:33.85 </td> <td class="ltx_td ltx_align_justify ltx_align_top" id="S5.T2.41.157.115.4" style="padding-left:2.0pt;padding-right:2.0pt;"> -02:46:50.01 </td> <td class="ltx_td ltx_align_left" id="S5.T2.41.157.115.5" style="padding-left:2.0pt;padding-right:2.0pt;">SNIa-91T-like</td> <td class="ltx_td ltx_align_center" id="S5.T2.41.157.115.6" style="padding-left:2.0pt;padding-right:2.0pt;">✓</td> <td class="ltx_td ltx_align_top" id="S5.T2.41.157.115.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> <tr class="ltx_tr" id="S5.T2.41.158.116"> <td class="ltx_td ltx_nopad_l ltx_align_left ltx_border_t" id="S5.T2.41.158.116.1" style="padding-left:2.0pt;padding-right:2.0pt;"> 155 \insertTableNotes </td> <td class="ltx_td ltx_align_justify ltx_align_top ltx_border_t" id="S5.T2.41.158.116.2" style="padding-left:2.0pt;padding-right:2.0pt;"></td> <td class="ltx_td ltx_align_justify ltx_align_top ltx_border_t" id="S5.T2.41.158.116.3" style="padding-left:2.0pt;padding-right:2.0pt;"></td> <td class="ltx_td ltx_align_justify ltx_align_top ltx_border_t" id="S5.T2.41.158.116.4" style="padding-left:2.0pt;padding-right:2.0pt;"></td> <td class="ltx_td ltx_border_t" id="S5.T2.41.158.116.5" style="padding-left:2.0pt;padding-right:2.0pt;"></td> <td class="ltx_td ltx_border_t" id="S5.T2.41.158.116.6" style="padding-left:2.0pt;padding-right:2.0pt;"></td> <td class="ltx_td ltx_align_justify ltx_align_top ltx_border_t" id="S5.T2.41.158.116.7" style="padding-left:2.0pt;padding-right:2.0pt;"></td> </tr> </tbody> </table> </figure> </section> <section class="ltx_section" id="Sx1"> <h2 class="ltx_title ltx_title_section">Acknowledgements</h2> <div class="ltx_para" id="Sx1.p1"> We thank Julien Peloton for assistance in retrieving data from Fink. P.J.P. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon Europe research and innovation program (grant agreement No. 10104229 – TransPIre). EEH is supported by a Gates Cambridge Scholarship (#OPP1144). This work is a result of the COIN Residence Program #7111111<a class="ltx_ref ltx_url ltx_font_typewriter" href="https://cosmostatistics-initiative.org/residence-programs/crp7/" title="">https://cosmostatistics-initiative.org/residence-programs/crp7/</a>, held in Lisbon, Portugal, from 9 to 16 September 2023 and supported by the Portuguese Fundação para a Ciência e a Tecnologia (FCT) through the Strategic Programme UIDP/FIS/00099/2020 and UIDB/FIS/00099/2020 for CENTRA. The Cosmostatistics Initiative (COIN, <a class="ltx_ref ltx_url ltx_font_typewriter" href="https://cosmostatistics-initiative.org/" title="">https://cosmostatistics-initiative.org/</a>) is an international network of researchers whose goal is to foster interdisciplinarity inspired by astronomy. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research has made use of “Aladin sky atlas” developed at CDS, Strasbourg Observatory, France. This work made use of Astropy (<a class="ltx_ref ltx_url ltx_font_typewriter" href="http://www.astropy.org" title="">http://www.astropy.org</a>) a community-developed core Python package and an ecosystem of tools and resources for astronomy <cite class="ltx_cite ltx_citemacro_citep">(Astropy Collaboration et al. <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib3" title="">2013</a>, <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib2" title="">2018</a>, <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib1" title="">2022</a>)</cite>. The ELEPHANT icon was taken from <a class="ltx_ref ltx_url ltx_font_typewriter" href="https://icons8.com" title="">https://icons8.com</a>. The color palette used in this work was inspired by “The Temptation of St. Anthony” by Salvador Dali, 1946. </div> </section> <section class="ltx_section" id="Sx2"> <h2 class="ltx_title ltx_title_section">Data Availability</h2> <div class="ltx_para" id="Sx2.p1"> The data used here can be accessed via the Fink data transfer service: <a class="ltx_ref ltx_url ltx_font_typewriter" href="https://fink-portal.org/download" title="">https://fink-portal.org/download</a>. The ELEPHANT pipeline is publicly available on github: <a class="ltx_ref ltx_url ltx_font_typewriter" href="https://github.com/COINtoolbox/extragalactic_hostless" title="">https://github.com/COINtoolbox/extragalactic_hostless</a>. </div> </section> <section class="ltx_bibliography" id="bib"> <h2 class="ltx_title ltx_title_bibliography">References</h2> <ul class="ltx_biblist"> <li class="ltx_bibitem" id="bib.bib1"> Astropy Collaboration et al. (2022) Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, ApJ, 935, 167 </li> <li class="ltx_bibitem" id="bib.bib2"> Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123 </li> <li class="ltx_bibitem" id="bib.bib3"> Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33 </li> <li class="ltx_bibitem" id="bib.bib4"> Balboa & Grzywacz (2003) Balboa, R. M. & Grzywacz, N. M. 2003, Vision Research, 43, 2527 </li> <li class="ltx_bibitem" id="bib.bib5"> Baldwin et al. (1981) Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5 </li> <li class="ltx_bibitem" id="bib.bib6"> Bellm et al. (2019) Bellm, E., Blum, R., Graham, M., et al. 2019, LDM-612, Plans and Policies for LSST Alert Distribution, <a class="ltx_ref ltx_url ltx_font_typewriter" href="https://ls.st/ldm-612" title="">https://ls.st/ldm-612</a> </li> <li class="ltx_bibitem" id="bib.bib7"> Bellm et al. (2019) Bellm, E. C., Kulkarni, S. R., Graham, M. J., et al. 2019, PASP, 131, 018002 </li> <li class="ltx_bibitem" id="bib.bib8"> Bertin & Arnouts (1996) Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393 </li> <li class="ltx_bibitem" id="bib.bib9"> Biswas et al. (2023) Biswas, B., Ishida, E. E. O., Peloton, J., et al. 2023, A&A, 677, A77 </li> <li class="ltx_bibitem" id="bib.bib10"> Bonnarel et al. (2000) Bonnarel, F., Fernique, P., Bienaymé, O., et al. 2000, A&AS, 143, 33 </li> <li class="ltx_bibitem" id="bib.bib11"> Chen et al. (2023) Chen, Z. H., Yan, L., Kangas, T., et al. 2023, ApJ, 943, 41 </li> <li class="ltx_bibitem" id="bib.bib12"> Davis et al. (2023) Davis, K. W., Taggart, K., Tinyanont, S., et al. 2023, MNRAS, 523, 2530 </li> <li class="ltx_bibitem" id="bib.bib13"> Drout et al. (2014) Drout, M. R., Chornock, R., Soderberg, A. M., et al. 2014, ApJ, 794, 23 </li> <li class="ltx_bibitem" id="bib.bib14"> Ducoin et al. (2020) Ducoin, J. G., Corre, D., Leroy, N., & Le Floch, E. 2020, MNRAS, 492, 4768 </li> <li class="ltx_bibitem" id="bib.bib15"> Filippenko (1997) Filippenko, A. V. 1997, ARA&A, 35, 309 </li> <li class="ltx_bibitem" id="bib.bib16"> Förster et al. (2021) Förster, F., Cabrera-Vives, G., Castillo-Navarrete, E., et al. 2021, AJ, 161, 242 </li> <li class="ltx_bibitem" id="bib.bib17"> Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1 </li> <li class="ltx_bibitem" id="bib.bib18"> Gal-Yam (2012) Gal-Yam, A. 2012, in Death of Massive Stars: Supernovae and Gamma-Ray Bursts, ed. P. Roming, N. Kawai, & E. Pian, Vol. 279, 253–260 </li> <li class="ltx_bibitem" id="bib.bib19"> Garcia-Zamora et al. (2018) Garcia-Zamora, E. M., Hernandez-Garcia, A., Mallorquin, M., et al. 2018, The Astronomer’s Telegram, 12344, 1 </li> <li class="ltx_bibitem" id="bib.bib20"> Gillanders et al. (2024) Gillanders, J. H., Rhodes, L., Srivastav, S., et al. 2024, arXiv e-prints, arXiv:2404.10660 </li> <li class="ltx_bibitem" id="bib.bib21"> Gilmozzi & Spyromilio (2007) Gilmozzi, R. & Spyromilio, J. 2007, The Messenger, 127, 11 </li> <li class="ltx_bibitem" id="bib.bib22"> Gomez et al. (2023) Gomez, S., Berger, E., Blanchard, P. K., et al. 2023, ApJ, 949, 114 </li> <li class="ltx_bibitem" id="bib.bib23"> Gomez et al. (2020) Gomez, S., Berger, E., Blanchard, P. K., et al. 2020, ApJ, 904, 74 </li> <li class="ltx_bibitem" id="bib.bib24"> Graham et al. (2015) Graham, M. L., Sand, D. J., Zaritsky, D., & Pritchet, C. J. 2015, ApJ, 807, 83 </li> <li class="ltx_bibitem" id="bib.bib25"> Hambleton et al. (2023) Hambleton, K. M., Bianco, F. B., Street, R., et al. 2023, PASP, 135, 105002 </li> <li class="ltx_bibitem" id="bib.bib26"> Ho et al. (2020) Ho, A. Y. Q., Perley, D. A., Beniamini, P., et al. 2020, ApJ, 905, 98 </li> <li class="ltx_bibitem" id="bib.bib27"> Johns et al. (2012) Johns, M., McCarthy, P., Raybould, K., et al. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8444, Ground-based and Airborne Telescopes IV, ed. L. M. Stepp, R. Gilmozzi, & H. J. Hall, 84441H </li> <li class="ltx_bibitem" id="bib.bib28"> Kankare et al. (2017) Kankare, E., Kotak, R., Mattila, S., et al. 2017, Nature Astronomy, 1, 865 </li> <li class="ltx_bibitem" id="bib.bib29"> Kasen et al. (2011) Kasen, D., Woosley, S. E., & Heger, A. 2011, ApJ, 734, 102 </li> <li class="ltx_bibitem" id="bib.bib30"> Kemper et al. (2010) Kemper, F., Woods, P. M., Antoniou, V., et al. 2010, PASP, 122, 683 </li> <li class="ltx_bibitem" id="bib.bib31"> Leoni et al. (2022) Leoni, M., Ishida, E. E. O., Peloton, J., & Möller, A. 2022, A&A, 663, A13 </li> <li class="ltx_bibitem" id="bib.bib32"> LSST Science Collaboration et al. (2009) LSST Science Collaboration, Abell, P. A., Allison, J., et al. 2009, arXiv e-prints, arXiv:0912.0201 </li> <li class="ltx_bibitem" id="bib.bib33"> Lunnan et al. (2020) Lunnan, R., Yan, L., Perley, D. A., et al. 2020, ApJ, 901, 61 </li> <li class="ltx_bibitem" id="bib.bib34"> Magain et al. (2005) Magain, P., Letawe, G., Courbin, F., et al. 2005, Nature, 437, 381 </li> <li class="ltx_bibitem" id="bib.bib35"> Martin (2006) Martin, J. C. 2006, AJ, 131, 3047 </li> <li class="ltx_bibitem" id="bib.bib36"> Masci et al. (2019) Masci, F. J., Laher, R. R., Rusholme, B., et al. 2019, PASP, 131, 018003 </li> <li class="ltx_bibitem" id="bib.bib37"> Matheson et al. (2021) Matheson, T., Stubens, C., Wolf, N., et al. 2021, AJ, 161, 107 </li> <li class="ltx_bibitem" id="bib.bib38"> McCrum et al. (2015) McCrum, M., Smartt, S. J., Rest, A., et al. 2015, MNRAS, 448, 1206 </li> <li class="ltx_bibitem" id="bib.bib39"> Möller & de Boissière (2020) Möller, A. & de Boissière, T. 2020, MNRAS, 491, 4277 </li> <li class="ltx_bibitem" id="bib.bib40"> Möller et al. (2021) Möller, A., Peloton, J., Ishida, E. E. O., et al. 2021, MNRAS, 501, 3272 </li> <li class="ltx_bibitem" id="bib.bib41"> Nordin et al. (2019) Nordin, J., Brinnel, V., van Santen, J., et al. 2019, A&A, 631, A147 </li> <li class="ltx_bibitem" id="bib.bib42"> Qin et al. (2024) Qin, Y.-J., Zabludoff, A., Arcavi, I., et al. 2024, MNRAS </li> <li class="ltx_bibitem" id="bib.bib43"> Qin et al. (2022) Qin, Y.-J., Zabludoff, A., Kisley, M., et al. 2022, ApJS, 259, 13 </li> <li class="ltx_bibitem" id="bib.bib44"> Reyes-Jainaga et al. (2023) Reyes-Jainaga, I., Förster, F., Muñoz Arancibia, A. M., et al. 2023, ApJ, 952, L43 </li> <li class="ltx_bibitem" id="bib.bib45"> Ryczanowski et al. (2020) Ryczanowski, D., Smith, G. P., Bianconi, M., et al. 2020, MNRAS, 495, 1666 </li> <li class="ltx_bibitem" id="bib.bib46"> Schulze et al. (2024) Schulze, S., Fransson, C., Kozyreva, A., et al. 2024, A&A, 683, A223 </li> <li class="ltx_bibitem" id="bib.bib47"> Shappee et al. (2014) Shappee, B., Prieto, J., Stanek, K. Z., et al. 2014, in American Astronomical Society Meeting Abstracts, Vol. 223, American Astronomical Society Meeting Abstracts #223, 236.03 </li> <li class="ltx_bibitem" id="bib.bib48"> Taggart & Perley (2021) Taggart, K. & Perley, D. A. 2021, MNRAS, 503, 3931 </li> <li class="ltx_bibitem" id="bib.bib49"> Tonry et al. (2018) Tonry, J. L., Denneau, L., Heinze, A. N., et al. 2018, PASP, 130, 064505 </li> <li class="ltx_bibitem" id="bib.bib50"> Wenger et al. (2000) Wenger, M., Ochsenbein, F., Egret, D., et al. 2000, A&AS, 143, 9 </li> <li class="ltx_bibitem" id="bib.bib51"> Williams et al. (2024) Williams, R. D., Francis, G. P., Lawrence, A., et al. 2024, arXiv e-prints, arXiv:2404.08315 </li> <li class="ltx_bibitem" id="bib.bib52"> Yamaoka (2017) Yamaoka, H. 2017, in Handbook of Supernovae, ed. A. W. Alsabti & P. Murdin, 29 </li> <li class="ltx_bibitem" id="bib.bib53"> Zinn et al. (2011) Zinn, P. C., Grunden, P., & Bomans, D. J. 2011, A&A, 536, A103 </li> <li class="ltx_bibitem" id="bib.bib54"> Zinn et al. (2012) Zinn, P. C., Stritzinger, M., Braithwaite, J., et al. 2012, A&A, 538, A30 </li> </ul> </section> <section class="ltx_appendix" id="A1"> <h2 class="ltx_title ltx_title_appendix"> Appendix A Nearest neighbor</h2> <div class="ltx_para" id="A1.p1"> To compute the distance from the transient to the nearest mask, we assume an origin position at the center of the image from where to calculate the distance. Masked pixels have value 1, whereas background pixels have value 0. To find the nearest masked pixel to the transient, we compare pixel by pixel until a mask is found. First, we check all adjacent pixels (including diagonally adjacent ones) related to the central pixel, starting from left to right and top to bottom. This process is repeated for outer layers until a masked pixel is found or we reach the limits of the 7-pixel threshold. If the distance between the central pixel and the nearest neighbor is not within a 7-pixel radius, we keep that alert in our sample for further checks. The Euclidean distance between the nearest masked pixel and the central pixel is included for the user to assess whether a neighbor is close enough for it to be considered an associated host. The algorithm works as follows: </div> <figure class="ltx_float ltx_algorithm" id="A1.29"> <div class="ltx_listing ltx_lst_numbers_left ltx_listing" id="A1.29.29"> <div class="ltx_listingline" id="A1.1.1.1"> Data: <math alttext="\boldsymbol{M}" class="ltx_Math" display="inline" id="A1.1.1.1.m1.1"><semantics id="A1.1.1.1.m1.1a"><mi id="A1.1.1.1.m1.1.1" xref="A1.1.1.1.m1.1.1.cmml">𝑴</mi><annotation-xml encoding="MathML-Content" id="A1.1.1.1.m1.1b"><ci id="A1.1.1.1.m1.1.1.cmml" xref="A1.1.1.1.m1.1.1">𝑴</ci></annotation-xml><annotation encoding="application/x-tex" id="A1.1.1.1.m1.1c">\boldsymbol{M}</annotation><annotation encoding="application/x-llamapun" id="A1.1.1.1.m1.1d">bold_italic_M</annotation></semantics></math>: Stamp of the segmented image </div> <div class="ltx_listingline" id="A1.2.2.2"> <math alttext="r" class="ltx_Math" display="inline" id="A1.2.2.2.m1.1"><semantics id="A1.2.2.2.m1.1a"><mi id="A1.2.2.2.m1.1.1" xref="A1.2.2.2.m1.1.1.cmml">r</mi><annotation-xml encoding="MathML-Content" id="A1.2.2.2.m1.1b"><ci id="A1.2.2.2.m1.1.1.cmml" xref="A1.2.2.2.m1.1.1">𝑟</ci></annotation-xml><annotation encoding="application/x-tex" id="A1.2.2.2.m1.1c">r</annotation><annotation encoding="application/x-llamapun" id="A1.2.2.2.m1.1d">italic_r</annotation></semantics></math>: Maximum radius for nearest detected source </div> <div class="ltx_listingline" id="A1.3.3.3"> Result: <math alttext="x_{1}" class="ltx_Math" display="inline" id="A1.3.3.3.m1.1"><semantics id="A1.3.3.3.m1.1a"><msub id="A1.3.3.3.m1.1.1" xref="A1.3.3.3.m1.1.1.cmml"><mi id="A1.3.3.3.m1.1.1.2" xref="A1.3.3.3.m1.1.1.2.cmml">x</mi><mn id="A1.3.3.3.m1.1.1.3" xref="A1.3.3.3.m1.1.1.3.cmml">1</mn></msub><annotation-xml encoding="MathML-Content" id="A1.3.3.3.m1.1b"><apply id="A1.3.3.3.m1.1.1.cmml" xref="A1.3.3.3.m1.1.1"><csymbol cd="ambiguous" id="A1.3.3.3.m1.1.1.1.cmml" xref="A1.3.3.3.m1.1.1">subscript</csymbol><ci id="A1.3.3.3.m1.1.1.2.cmml" xref="A1.3.3.3.m1.1.1.2">𝑥</ci><cn id="A1.3.3.3.m1.1.1.3.cmml" type="integer" xref="A1.3.3.3.m1.1.1.3">1</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.3.3.3.m1.1c">x_{1}</annotation><annotation encoding="application/x-llamapun" id="A1.3.3.3.m1.1d">italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT</annotation></semantics></math>: x-axis index of the closest masked source </div> <div class="ltx_listingline" id="A1.4.4.4"> <math alttext="x_{2}" class="ltx_Math" display="inline" id="A1.4.4.4.m1.1"><semantics id="A1.4.4.4.m1.1a"><msub id="A1.4.4.4.m1.1.1" xref="A1.4.4.4.m1.1.1.cmml"><mi id="A1.4.4.4.m1.1.1.2" xref="A1.4.4.4.m1.1.1.2.cmml">x</mi><mn id="A1.4.4.4.m1.1.1.3" xref="A1.4.4.4.m1.1.1.3.cmml">2</mn></msub><annotation-xml encoding="MathML-Content" id="A1.4.4.4.m1.1b"><apply id="A1.4.4.4.m1.1.1.cmml" xref="A1.4.4.4.m1.1.1"><csymbol cd="ambiguous" id="A1.4.4.4.m1.1.1.1.cmml" xref="A1.4.4.4.m1.1.1">subscript</csymbol><ci id="A1.4.4.4.m1.1.1.2.cmml" xref="A1.4.4.4.m1.1.1.2">𝑥</ci><cn id="A1.4.4.4.m1.1.1.3.cmml" type="integer" xref="A1.4.4.4.m1.1.1.3">2</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.4.4.4.m1.1c">x_{2}</annotation><annotation encoding="application/x-llamapun" id="A1.4.4.4.m1.1d">italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT</annotation></semantics></math>: y-axis index of the closest masked source </div> <div class="ltx_listingline" id="A1.5.5.5"> <math alttext="\delta" class="ltx_Math" display="inline" id="A1.5.5.5.m1.1"><semantics id="A1.5.5.5.m1.1a"><mi id="A1.5.5.5.m1.1.1" xref="A1.5.5.5.m1.1.1.cmml">δ</mi><annotation-xml encoding="MathML-Content" id="A1.5.5.5.m1.1b"><ci id="A1.5.5.5.m1.1.1.cmml" xref="A1.5.5.5.m1.1.1">𝛿</ci></annotation-xml><annotation encoding="application/x-tex" id="A1.5.5.5.m1.1c">\delta</annotation><annotation encoding="application/x-llamapun" id="A1.5.5.5.m1.1d">italic_δ</annotation></semantics></math>: Euclidean distance measured in image pixels </div> <div class="ltx_listingline" id="A1.6.6.6"> <math alttext="f" class="ltx_Math" display="inline" id="A1.6.6.6.m1.1"><semantics id="A1.6.6.6.m1.1a"><mi id="A1.6.6.6.m1.1.1" xref="A1.6.6.6.m1.1.1.cmml">f</mi><annotation-xml encoding="MathML-Content" id="A1.6.6.6.m1.1b"><ci id="A1.6.6.6.m1.1.1.cmml" xref="A1.6.6.6.m1.1.1">𝑓</ci></annotation-xml><annotation encoding="application/x-tex" id="A1.6.6.6.m1.1c">f</annotation><annotation encoding="application/x-llamapun" id="A1.6.6.6.m1.1d">italic_f</annotation></semantics></math>: Flag (true for hostless, zero otherwise) </div> <div class="ltx_listingline" id="A1.7.7.7"> <math alttext="\boldsymbol{M}_{\textup{>0}}\leftarrow 1" class="ltx_Math" display="inline" id="A1.7.7.7.m1.1"><semantics id="A1.7.7.7.m1.1a"><mrow id="A1.7.7.7.m1.1.1" xref="A1.7.7.7.m1.1.1.cmml"><msub id="A1.7.7.7.m1.1.1.2" xref="A1.7.7.7.m1.1.1.2.cmml"><mi id="A1.7.7.7.m1.1.1.2.2" xref="A1.7.7.7.m1.1.1.2.2.cmml">𝑴</mi><mtext id="A1.7.7.7.m1.1.1.2.3" xref="A1.7.7.7.m1.1.1.2.3a.cmml">¿0</mtext></msub><mo id="A1.7.7.7.m1.1.1.1" stretchy="false" xref="A1.7.7.7.m1.1.1.1.cmml">←</mo><mn id="A1.7.7.7.m1.1.1.3" xref="A1.7.7.7.m1.1.1.3.cmml">1</mn></mrow><annotation-xml encoding="MathML-Content" id="A1.7.7.7.m1.1b"><apply id="A1.7.7.7.m1.1.1.cmml" xref="A1.7.7.7.m1.1.1"><ci id="A1.7.7.7.m1.1.1.1.cmml" xref="A1.7.7.7.m1.1.1.1">←</ci><apply id="A1.7.7.7.m1.1.1.2.cmml" xref="A1.7.7.7.m1.1.1.2"><csymbol cd="ambiguous" id="A1.7.7.7.m1.1.1.2.1.cmml" xref="A1.7.7.7.m1.1.1.2">subscript</csymbol><ci id="A1.7.7.7.m1.1.1.2.2.cmml" xref="A1.7.7.7.m1.1.1.2.2">𝑴</ci><ci id="A1.7.7.7.m1.1.1.2.3a.cmml" xref="A1.7.7.7.m1.1.1.2.3"><mtext id="A1.7.7.7.m1.1.1.2.3.cmml" mathsize="70%" xref="A1.7.7.7.m1.1.1.2.3">¿0</mtext></ci></apply><cn id="A1.7.7.7.m1.1.1.3.cmml" type="integer" xref="A1.7.7.7.m1.1.1.3">1</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.7.7.7.m1.1c">\boldsymbol{M}_{\textup{>0}}\leftarrow 1</annotation><annotation encoding="application/x-llamapun" id="A1.7.7.7.m1.1d">bold_italic_M start_POSTSUBSCRIPT ¿0 end_POSTSUBSCRIPT ← 1</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.8.8.8"> <math alttext="\tau,\delta,f\leftarrow 30,100,\textup{True}" class="ltx_Math" display="inline" id="A1.8.8.8.m1.7"><semantics id="A1.8.8.8.m1.7a"><mrow id="A1.8.8.8.m1.7.7.2" xref="A1.8.8.8.m1.7.7.3.cmml"><mrow id="A1.8.8.8.m1.6.6.1.1" xref="A1.8.8.8.m1.6.6.1.1.cmml"><mrow id="A1.8.8.8.m1.6.6.1.1.2.2" xref="A1.8.8.8.m1.6.6.1.1.2.1.cmml"><mi id="A1.8.8.8.m1.1.1" xref="A1.8.8.8.m1.1.1.cmml">τ</mi><mo id="A1.8.8.8.m1.6.6.1.1.2.2.1" xref="A1.8.8.8.m1.6.6.1.1.2.1.cmml">,</mo><mi id="A1.8.8.8.m1.2.2" xref="A1.8.8.8.m1.2.2.cmml">δ</mi><mo id="A1.8.8.8.m1.6.6.1.1.2.2.2" xref="A1.8.8.8.m1.6.6.1.1.2.1.cmml">,</mo><mi id="A1.8.8.8.m1.3.3" xref="A1.8.8.8.m1.3.3.cmml">f</mi></mrow><mo id="A1.8.8.8.m1.6.6.1.1.1" stretchy="false" xref="A1.8.8.8.m1.6.6.1.1.1.cmml">←</mo><mn id="A1.8.8.8.m1.6.6.1.1.3" xref="A1.8.8.8.m1.6.6.1.1.3.cmml">30</mn></mrow><mo id="A1.8.8.8.m1.7.7.2.3" xref="A1.8.8.8.m1.7.7.3a.cmml">,</mo><mrow id="A1.8.8.8.m1.7.7.2.2.2" xref="A1.8.8.8.m1.7.7.2.2.1.cmml"><mn id="A1.8.8.8.m1.4.4" xref="A1.8.8.8.m1.4.4.cmml">100</mn><mo id="A1.8.8.8.m1.7.7.2.2.2.1" xref="A1.8.8.8.m1.7.7.2.2.1.cmml">,</mo><mtext id="A1.8.8.8.m1.5.5" xref="A1.8.8.8.m1.5.5a.cmml">True</mtext></mrow></mrow><annotation-xml encoding="MathML-Content" id="A1.8.8.8.m1.7b"><apply id="A1.8.8.8.m1.7.7.3.cmml" xref="A1.8.8.8.m1.7.7.2"><csymbol cd="ambiguous" id="A1.8.8.8.m1.7.7.3a.cmml" xref="A1.8.8.8.m1.7.7.2.3">formulae-sequence</csymbol><apply id="A1.8.8.8.m1.6.6.1.1.cmml" xref="A1.8.8.8.m1.6.6.1.1"><ci id="A1.8.8.8.m1.6.6.1.1.1.cmml" xref="A1.8.8.8.m1.6.6.1.1.1">←</ci><list id="A1.8.8.8.m1.6.6.1.1.2.1.cmml" xref="A1.8.8.8.m1.6.6.1.1.2.2"><ci id="A1.8.8.8.m1.1.1.cmml" xref="A1.8.8.8.m1.1.1">𝜏</ci><ci id="A1.8.8.8.m1.2.2.cmml" xref="A1.8.8.8.m1.2.2">𝛿</ci><ci id="A1.8.8.8.m1.3.3.cmml" xref="A1.8.8.8.m1.3.3">𝑓</ci></list><cn id="A1.8.8.8.m1.6.6.1.1.3.cmml" type="integer" xref="A1.8.8.8.m1.6.6.1.1.3">30</cn></apply><list id="A1.8.8.8.m1.7.7.2.2.1.cmml" xref="A1.8.8.8.m1.7.7.2.2.2"><cn id="A1.8.8.8.m1.4.4.cmml" type="integer" xref="A1.8.8.8.m1.4.4">100</cn><ci id="A1.8.8.8.m1.5.5a.cmml" xref="A1.8.8.8.m1.5.5"><mtext id="A1.8.8.8.m1.5.5.cmml" xref="A1.8.8.8.m1.5.5">True</mtext></ci></list></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.8.8.8.m1.7c">\tau,\delta,f\leftarrow 30,100,\textup{True}</annotation><annotation encoding="application/x-llamapun" id="A1.8.8.8.m1.7d">italic_τ , italic_δ , italic_f ← 30 , 100 , True</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.9.9.9"> <math alttext="x_{1},x_{2}\leftarrow\textup{None}" class="ltx_Math" display="inline" id="A1.9.9.9.m1.2"><semantics id="A1.9.9.9.m1.2a"><mrow id="A1.9.9.9.m1.2.2" xref="A1.9.9.9.m1.2.2.cmml"><mrow id="A1.9.9.9.m1.2.2.2.2" xref="A1.9.9.9.m1.2.2.2.3.cmml"><msub id="A1.9.9.9.m1.1.1.1.1.1" xref="A1.9.9.9.m1.1.1.1.1.1.cmml"><mi id="A1.9.9.9.m1.1.1.1.1.1.2" xref="A1.9.9.9.m1.1.1.1.1.1.2.cmml">x</mi><mn id="A1.9.9.9.m1.1.1.1.1.1.3" xref="A1.9.9.9.m1.1.1.1.1.1.3.cmml">1</mn></msub><mo id="A1.9.9.9.m1.2.2.2.2.3" xref="A1.9.9.9.m1.2.2.2.3.cmml">,</mo><msub id="A1.9.9.9.m1.2.2.2.2.2" xref="A1.9.9.9.m1.2.2.2.2.2.cmml"><mi id="A1.9.9.9.m1.2.2.2.2.2.2" xref="A1.9.9.9.m1.2.2.2.2.2.2.cmml">x</mi><mn id="A1.9.9.9.m1.2.2.2.2.2.3" xref="A1.9.9.9.m1.2.2.2.2.2.3.cmml">2</mn></msub></mrow><mo id="A1.9.9.9.m1.2.2.3" stretchy="false" xref="A1.9.9.9.m1.2.2.3.cmml">←</mo><mtext id="A1.9.9.9.m1.2.2.4" xref="A1.9.9.9.m1.2.2.4a.cmml">None</mtext></mrow><annotation-xml encoding="MathML-Content" id="A1.9.9.9.m1.2b"><apply id="A1.9.9.9.m1.2.2.cmml" xref="A1.9.9.9.m1.2.2"><ci id="A1.9.9.9.m1.2.2.3.cmml" xref="A1.9.9.9.m1.2.2.3">←</ci><list id="A1.9.9.9.m1.2.2.2.3.cmml" xref="A1.9.9.9.m1.2.2.2.2"><apply id="A1.9.9.9.m1.1.1.1.1.1.cmml" xref="A1.9.9.9.m1.1.1.1.1.1"><csymbol cd="ambiguous" id="A1.9.9.9.m1.1.1.1.1.1.1.cmml" xref="A1.9.9.9.m1.1.1.1.1.1">subscript</csymbol><ci id="A1.9.9.9.m1.1.1.1.1.1.2.cmml" xref="A1.9.9.9.m1.1.1.1.1.1.2">𝑥</ci><cn id="A1.9.9.9.m1.1.1.1.1.1.3.cmml" type="integer" xref="A1.9.9.9.m1.1.1.1.1.1.3">1</cn></apply><apply id="A1.9.9.9.m1.2.2.2.2.2.cmml" xref="A1.9.9.9.m1.2.2.2.2.2"><csymbol cd="ambiguous" id="A1.9.9.9.m1.2.2.2.2.2.1.cmml" xref="A1.9.9.9.m1.2.2.2.2.2">subscript</csymbol><ci id="A1.9.9.9.m1.2.2.2.2.2.2.cmml" xref="A1.9.9.9.m1.2.2.2.2.2.2">𝑥</ci><cn id="A1.9.9.9.m1.2.2.2.2.2.3.cmml" type="integer" xref="A1.9.9.9.m1.2.2.2.2.2.3">2</cn></apply></list><ci id="A1.9.9.9.m1.2.2.4a.cmml" xref="A1.9.9.9.m1.2.2.4"><mtext id="A1.9.9.9.m1.2.2.4.cmml" xref="A1.9.9.9.m1.2.2.4">None</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.9.9.9.m1.2c">x_{1},x_{2}\leftarrow\textup{None}</annotation><annotation encoding="application/x-llamapun" id="A1.9.9.9.m1.2d">italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ← None</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.10.10.10"> if <math alttext="\boldsymbol{M}_{\tau,\tau}=1" class="ltx_Math" display="inline" id="A1.10.10.10.1.m1.2"><semantics id="A1.10.10.10.1.m1.2a"><mrow id="A1.10.10.10.1.m1.2.3" xref="A1.10.10.10.1.m1.2.3.cmml"><msub id="A1.10.10.10.1.m1.2.3.2" xref="A1.10.10.10.1.m1.2.3.2.cmml"><mi id="A1.10.10.10.1.m1.2.3.2.2" xref="A1.10.10.10.1.m1.2.3.2.2.cmml">𝐌</mi><mrow id="A1.10.10.10.1.m1.2.2.2.4" xref="A1.10.10.10.1.m1.2.2.2.3.cmml"><mi id="A1.10.10.10.1.m1.1.1.1.1" xref="A1.10.10.10.1.m1.1.1.1.1.cmml">τ</mi><mo id="A1.10.10.10.1.m1.2.2.2.4.1" xref="A1.10.10.10.1.m1.2.2.2.3.cmml">,</mo><mi id="A1.10.10.10.1.m1.2.2.2.2" xref="A1.10.10.10.1.m1.2.2.2.2.cmml">τ</mi></mrow></msub><mo id="A1.10.10.10.1.m1.2.3.1" xref="A1.10.10.10.1.m1.2.3.1.cmml">=</mo><mn id="A1.10.10.10.1.m1.2.3.3" xref="A1.10.10.10.1.m1.2.3.3.cmml">1</mn></mrow><annotation-xml encoding="MathML-Content" id="A1.10.10.10.1.m1.2b"><apply id="A1.10.10.10.1.m1.2.3.cmml" xref="A1.10.10.10.1.m1.2.3"><eq id="A1.10.10.10.1.m1.2.3.1.cmml" xref="A1.10.10.10.1.m1.2.3.1"></eq><apply id="A1.10.10.10.1.m1.2.3.2.cmml" xref="A1.10.10.10.1.m1.2.3.2"><csymbol cd="ambiguous" id="A1.10.10.10.1.m1.2.3.2.1.cmml" xref="A1.10.10.10.1.m1.2.3.2">subscript</csymbol><ci id="A1.10.10.10.1.m1.2.3.2.2.cmml" xref="A1.10.10.10.1.m1.2.3.2.2">𝐌</ci><list id="A1.10.10.10.1.m1.2.2.2.3.cmml" xref="A1.10.10.10.1.m1.2.2.2.4"><ci id="A1.10.10.10.1.m1.1.1.1.1.cmml" xref="A1.10.10.10.1.m1.1.1.1.1">𝜏</ci><ci id="A1.10.10.10.1.m1.2.2.2.2.cmml" xref="A1.10.10.10.1.m1.2.2.2.2">𝜏</ci></list></apply><cn id="A1.10.10.10.1.m1.2.3.3.cmml" type="integer" xref="A1.10.10.10.1.m1.2.3.3">1</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.10.10.10.1.m1.2c">\boldsymbol{M}_{\tau,\tau}=1</annotation><annotation encoding="application/x-llamapun" id="A1.10.10.10.1.m1.2d">bold_italic_M start_POSTSUBSCRIPT italic_τ , italic_τ end_POSTSUBSCRIPT = 1</annotation></semantics></math> then </div> <div class="ltx_listingline" id="A1.11.11.11"> <math alttext="f\leftarrow\textup{False}" class="ltx_Math" display="inline" id="A1.11.11.11.m1.1"><semantics id="A1.11.11.11.m1.1a"><mrow id="A1.11.11.11.m1.1.1" xref="A1.11.11.11.m1.1.1.cmml"><mi id="A1.11.11.11.m1.1.1.2" xref="A1.11.11.11.m1.1.1.2.cmml">f</mi><mo id="A1.11.11.11.m1.1.1.1" stretchy="false" xref="A1.11.11.11.m1.1.1.1.cmml">←</mo><mtext id="A1.11.11.11.m1.1.1.3" xref="A1.11.11.11.m1.1.1.3a.cmml">False</mtext></mrow><annotation-xml encoding="MathML-Content" id="A1.11.11.11.m1.1b"><apply id="A1.11.11.11.m1.1.1.cmml" xref="A1.11.11.11.m1.1.1"><ci id="A1.11.11.11.m1.1.1.1.cmml" xref="A1.11.11.11.m1.1.1.1">←</ci><ci id="A1.11.11.11.m1.1.1.2.cmml" xref="A1.11.11.11.m1.1.1.2">𝑓</ci><ci id="A1.11.11.11.m1.1.1.3a.cmml" xref="A1.11.11.11.m1.1.1.3"><mtext id="A1.11.11.11.m1.1.1.3.cmml" xref="A1.11.11.11.m1.1.1.3">False</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.11.11.11.m1.1c">f\leftarrow\textup{False}</annotation><annotation encoding="application/x-llamapun" id="A1.11.11.11.m1.1d">italic_f ← False</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.12.12.12"> return <math alttext="\tau,\tau,0,f" class="ltx_Math" display="inline" id="A1.12.12.12.m1.4"><semantics id="A1.12.12.12.m1.4a"><mrow id="A1.12.12.12.m1.4.5.2" xref="A1.12.12.12.m1.4.5.1.cmml"><mi id="A1.12.12.12.m1.1.1" xref="A1.12.12.12.m1.1.1.cmml">τ</mi><mo id="A1.12.12.12.m1.4.5.2.1" xref="A1.12.12.12.m1.4.5.1.cmml">,</mo><mi id="A1.12.12.12.m1.2.2" xref="A1.12.12.12.m1.2.2.cmml">τ</mi><mo id="A1.12.12.12.m1.4.5.2.2" xref="A1.12.12.12.m1.4.5.1.cmml">,</mo><mn id="A1.12.12.12.m1.3.3" xref="A1.12.12.12.m1.3.3.cmml">0</mn><mo id="A1.12.12.12.m1.4.5.2.3" xref="A1.12.12.12.m1.4.5.1.cmml">,</mo><mi id="A1.12.12.12.m1.4.4" xref="A1.12.12.12.m1.4.4.cmml">f</mi></mrow><annotation-xml encoding="MathML-Content" id="A1.12.12.12.m1.4b"><list id="A1.12.12.12.m1.4.5.1.cmml" xref="A1.12.12.12.m1.4.5.2"><ci id="A1.12.12.12.m1.1.1.cmml" xref="A1.12.12.12.m1.1.1">𝜏</ci><ci id="A1.12.12.12.m1.2.2.cmml" xref="A1.12.12.12.m1.2.2">𝜏</ci><cn id="A1.12.12.12.m1.3.3.cmml" type="integer" xref="A1.12.12.12.m1.3.3">0</cn><ci id="A1.12.12.12.m1.4.4.cmml" xref="A1.12.12.12.m1.4.4">𝑓</ci></list></annotation-xml><annotation encoding="application/x-tex" id="A1.12.12.12.m1.4c">\tau,\tau,0,f</annotation><annotation encoding="application/x-llamapun" id="A1.12.12.12.m1.4d">italic_τ , italic_τ , 0 , italic_f</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.29.29.30"> else </div> <div class="ltx_listingline" id="A1.13.13.13"> for <math alttext="s\in\{1,\dots,r+1\}" class="ltx_Math" display="inline" id="A1.13.13.13.1.m1.3"><semantics id="A1.13.13.13.1.m1.3a"><mrow id="A1.13.13.13.1.m1.3.3" xref="A1.13.13.13.1.m1.3.3.cmml"><mi id="A1.13.13.13.1.m1.3.3.3" xref="A1.13.13.13.1.m1.3.3.3.cmml">s</mi><mo id="A1.13.13.13.1.m1.3.3.2" xref="A1.13.13.13.1.m1.3.3.2.cmml">∈</mo><mrow id="A1.13.13.13.1.m1.3.3.1.1" xref="A1.13.13.13.1.m1.3.3.1.2.cmml"><mo id="A1.13.13.13.1.m1.3.3.1.1.2" stretchy="false" xref="A1.13.13.13.1.m1.3.3.1.2.cmml">{</mo><mn id="A1.13.13.13.1.m1.1.1" xref="A1.13.13.13.1.m1.1.1.cmml">1</mn><mo id="A1.13.13.13.1.m1.3.3.1.1.3" xref="A1.13.13.13.1.m1.3.3.1.2.cmml">,</mo><mi id="A1.13.13.13.1.m1.2.2" mathvariant="normal" xref="A1.13.13.13.1.m1.2.2.cmml">…</mi><mo id="A1.13.13.13.1.m1.3.3.1.1.4" xref="A1.13.13.13.1.m1.3.3.1.2.cmml">,</mo><mrow id="A1.13.13.13.1.m1.3.3.1.1.1" xref="A1.13.13.13.1.m1.3.3.1.1.1.cmml"><mi id="A1.13.13.13.1.m1.3.3.1.1.1.2" xref="A1.13.13.13.1.m1.3.3.1.1.1.2.cmml">r</mi><mo id="A1.13.13.13.1.m1.3.3.1.1.1.1" xref="A1.13.13.13.1.m1.3.3.1.1.1.1.cmml">+</mo><mn id="A1.13.13.13.1.m1.3.3.1.1.1.3" xref="A1.13.13.13.1.m1.3.3.1.1.1.3.cmml">1</mn></mrow><mo id="A1.13.13.13.1.m1.3.3.1.1.5" stretchy="false" xref="A1.13.13.13.1.m1.3.3.1.2.cmml">}</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="A1.13.13.13.1.m1.3b"><apply id="A1.13.13.13.1.m1.3.3.cmml" xref="A1.13.13.13.1.m1.3.3"><in id="A1.13.13.13.1.m1.3.3.2.cmml" xref="A1.13.13.13.1.m1.3.3.2"></in><ci id="A1.13.13.13.1.m1.3.3.3.cmml" xref="A1.13.13.13.1.m1.3.3.3">𝑠</ci><set id="A1.13.13.13.1.m1.3.3.1.2.cmml" xref="A1.13.13.13.1.m1.3.3.1.1"><cn id="A1.13.13.13.1.m1.1.1.cmml" type="integer" xref="A1.13.13.13.1.m1.1.1">1</cn><ci id="A1.13.13.13.1.m1.2.2.cmml" xref="A1.13.13.13.1.m1.2.2">…</ci><apply id="A1.13.13.13.1.m1.3.3.1.1.1.cmml" xref="A1.13.13.13.1.m1.3.3.1.1.1"><plus id="A1.13.13.13.1.m1.3.3.1.1.1.1.cmml" xref="A1.13.13.13.1.m1.3.3.1.1.1.1"></plus><ci id="A1.13.13.13.1.m1.3.3.1.1.1.2.cmml" xref="A1.13.13.13.1.m1.3.3.1.1.1.2">𝑟</ci><cn id="A1.13.13.13.1.m1.3.3.1.1.1.3.cmml" type="integer" xref="A1.13.13.13.1.m1.3.3.1.1.1.3">1</cn></apply></set></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.13.13.13.1.m1.3c">s\in\{1,\dots,r+1\}</annotation><annotation encoding="application/x-llamapun" id="A1.13.13.13.1.m1.3d">italic_s ∈ { 1 , … , italic_r + 1 }</annotation></semantics></math> do </div> <div class="ltx_listingline" id="A1.14.14.14"> <math alttext="\boldsymbol{a}\leftarrow\{\tau-1-s,\tau+2+s\}" class="ltx_Math" display="inline" id="A1.14.14.14.m1.2"><semantics id="A1.14.14.14.m1.2a"><mrow id="A1.14.14.14.m1.2.2" xref="A1.14.14.14.m1.2.2.cmml"><mi id="A1.14.14.14.m1.2.2.4" xref="A1.14.14.14.m1.2.2.4.cmml">𝒂</mi><mo id="A1.14.14.14.m1.2.2.3" stretchy="false" xref="A1.14.14.14.m1.2.2.3.cmml">←</mo><mrow id="A1.14.14.14.m1.2.2.2.2" xref="A1.14.14.14.m1.2.2.2.3.cmml"><mo id="A1.14.14.14.m1.2.2.2.2.3" stretchy="false" xref="A1.14.14.14.m1.2.2.2.3.cmml">{</mo><mrow id="A1.14.14.14.m1.1.1.1.1.1" xref="A1.14.14.14.m1.1.1.1.1.1.cmml"><mi id="A1.14.14.14.m1.1.1.1.1.1.2" xref="A1.14.14.14.m1.1.1.1.1.1.2.cmml">τ</mi><mo id="A1.14.14.14.m1.1.1.1.1.1.1" xref="A1.14.14.14.m1.1.1.1.1.1.1.cmml">−</mo><mn id="A1.14.14.14.m1.1.1.1.1.1.3" xref="A1.14.14.14.m1.1.1.1.1.1.3.cmml">1</mn><mo id="A1.14.14.14.m1.1.1.1.1.1.1a" xref="A1.14.14.14.m1.1.1.1.1.1.1.cmml">−</mo><mi id="A1.14.14.14.m1.1.1.1.1.1.4" xref="A1.14.14.14.m1.1.1.1.1.1.4.cmml">s</mi></mrow><mo id="A1.14.14.14.m1.2.2.2.2.4" xref="A1.14.14.14.m1.2.2.2.3.cmml">,</mo><mrow id="A1.14.14.14.m1.2.2.2.2.2" xref="A1.14.14.14.m1.2.2.2.2.2.cmml"><mi id="A1.14.14.14.m1.2.2.2.2.2.2" xref="A1.14.14.14.m1.2.2.2.2.2.2.cmml">τ</mi><mo id="A1.14.14.14.m1.2.2.2.2.2.1" xref="A1.14.14.14.m1.2.2.2.2.2.1.cmml">+</mo><mn id="A1.14.14.14.m1.2.2.2.2.2.3" xref="A1.14.14.14.m1.2.2.2.2.2.3.cmml">2</mn><mo id="A1.14.14.14.m1.2.2.2.2.2.1a" xref="A1.14.14.14.m1.2.2.2.2.2.1.cmml">+</mo><mi id="A1.14.14.14.m1.2.2.2.2.2.4" xref="A1.14.14.14.m1.2.2.2.2.2.4.cmml">s</mi></mrow><mo id="A1.14.14.14.m1.2.2.2.2.5" stretchy="false" xref="A1.14.14.14.m1.2.2.2.3.cmml">}</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="A1.14.14.14.m1.2b"><apply id="A1.14.14.14.m1.2.2.cmml" xref="A1.14.14.14.m1.2.2"><ci id="A1.14.14.14.m1.2.2.3.cmml" xref="A1.14.14.14.m1.2.2.3">←</ci><ci id="A1.14.14.14.m1.2.2.4.cmml" xref="A1.14.14.14.m1.2.2.4">𝒂</ci><set id="A1.14.14.14.m1.2.2.2.3.cmml" xref="A1.14.14.14.m1.2.2.2.2"><apply id="A1.14.14.14.m1.1.1.1.1.1.cmml" xref="A1.14.14.14.m1.1.1.1.1.1"><minus id="A1.14.14.14.m1.1.1.1.1.1.1.cmml" xref="A1.14.14.14.m1.1.1.1.1.1.1"></minus><ci id="A1.14.14.14.m1.1.1.1.1.1.2.cmml" xref="A1.14.14.14.m1.1.1.1.1.1.2">𝜏</ci><cn id="A1.14.14.14.m1.1.1.1.1.1.3.cmml" type="integer" xref="A1.14.14.14.m1.1.1.1.1.1.3">1</cn><ci id="A1.14.14.14.m1.1.1.1.1.1.4.cmml" xref="A1.14.14.14.m1.1.1.1.1.1.4">𝑠</ci></apply><apply id="A1.14.14.14.m1.2.2.2.2.2.cmml" xref="A1.14.14.14.m1.2.2.2.2.2"><plus id="A1.14.14.14.m1.2.2.2.2.2.1.cmml" xref="A1.14.14.14.m1.2.2.2.2.2.1"></plus><ci id="A1.14.14.14.m1.2.2.2.2.2.2.cmml" xref="A1.14.14.14.m1.2.2.2.2.2.2">𝜏</ci><cn id="A1.14.14.14.m1.2.2.2.2.2.3.cmml" type="integer" xref="A1.14.14.14.m1.2.2.2.2.2.3">2</cn><ci id="A1.14.14.14.m1.2.2.2.2.2.4.cmml" xref="A1.14.14.14.m1.2.2.2.2.2.4">𝑠</ci></apply></set></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.14.14.14.m1.2c">\boldsymbol{a}\leftarrow\{\tau-1-s,\tau+2+s\}</annotation><annotation encoding="application/x-llamapun" id="A1.14.14.14.m1.2d">bold_italic_a ← { italic_τ - 1 - italic_s , italic_τ + 2 + italic_s }</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.15.15.15"> <math alttext="\nu\leftarrow 0" class="ltx_Math" display="inline" id="A1.15.15.15.m1.1"><semantics id="A1.15.15.15.m1.1a"><mrow id="A1.15.15.15.m1.1.1" xref="A1.15.15.15.m1.1.1.cmml"><mi id="A1.15.15.15.m1.1.1.2" xref="A1.15.15.15.m1.1.1.2.cmml">ν</mi><mo id="A1.15.15.15.m1.1.1.1" stretchy="false" xref="A1.15.15.15.m1.1.1.1.cmml">←</mo><mn id="A1.15.15.15.m1.1.1.3" xref="A1.15.15.15.m1.1.1.3.cmml">0</mn></mrow><annotation-xml encoding="MathML-Content" id="A1.15.15.15.m1.1b"><apply id="A1.15.15.15.m1.1.1.cmml" xref="A1.15.15.15.m1.1.1"><ci id="A1.15.15.15.m1.1.1.1.cmml" xref="A1.15.15.15.m1.1.1.1">←</ci><ci id="A1.15.15.15.m1.1.1.2.cmml" xref="A1.15.15.15.m1.1.1.2">𝜈</ci><cn id="A1.15.15.15.m1.1.1.3.cmml" type="integer" xref="A1.15.15.15.m1.1.1.3">0</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.15.15.15.m1.1c">\nu\leftarrow 0</annotation><annotation encoding="application/x-llamapun" id="A1.15.15.15.m1.1d">italic_ν ← 0</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.16.16.16"> for <math alttext="i\in\boldsymbol{a}" class="ltx_Math" display="inline" id="A1.16.16.16.1.m1.1"><semantics id="A1.16.16.16.1.m1.1a"><mrow id="A1.16.16.16.1.m1.1.1" xref="A1.16.16.16.1.m1.1.1.cmml"><mi id="A1.16.16.16.1.m1.1.1.2" xref="A1.16.16.16.1.m1.1.1.2.cmml">i</mi><mo id="A1.16.16.16.1.m1.1.1.1" xref="A1.16.16.16.1.m1.1.1.1.cmml">∈</mo><mi id="A1.16.16.16.1.m1.1.1.3" xref="A1.16.16.16.1.m1.1.1.3.cmml">𝐚</mi></mrow><annotation-xml encoding="MathML-Content" id="A1.16.16.16.1.m1.1b"><apply id="A1.16.16.16.1.m1.1.1.cmml" xref="A1.16.16.16.1.m1.1.1"><in id="A1.16.16.16.1.m1.1.1.1.cmml" xref="A1.16.16.16.1.m1.1.1.1"></in><ci id="A1.16.16.16.1.m1.1.1.2.cmml" xref="A1.16.16.16.1.m1.1.1.2">𝑖</ci><ci id="A1.16.16.16.1.m1.1.1.3.cmml" xref="A1.16.16.16.1.m1.1.1.3">𝐚</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.16.16.16.1.m1.1c">i\in\boldsymbol{a}</annotation><annotation encoding="application/x-llamapun" id="A1.16.16.16.1.m1.1d">italic_i ∈ bold_italic_a</annotation></semantics></math> do </div> <div class="ltx_listingline" id="A1.17.17.17"> if <math alttext="(\nu=0)\lor(\nu=\tau+1+s)" class="ltx_Math" display="inline" id="A1.17.17.17.1.m1.2"><semantics id="A1.17.17.17.1.m1.2a"><mrow id="A1.17.17.17.1.m1.2.2" xref="A1.17.17.17.1.m1.2.2.cmml"><mrow id="A1.17.17.17.1.m1.1.1.1.1" xref="A1.17.17.17.1.m1.1.1.1.1.1.cmml"><mo id="A1.17.17.17.1.m1.1.1.1.1.2" stretchy="false" xref="A1.17.17.17.1.m1.1.1.1.1.1.cmml">(</mo><mrow id="A1.17.17.17.1.m1.1.1.1.1.1" xref="A1.17.17.17.1.m1.1.1.1.1.1.cmml"><mi id="A1.17.17.17.1.m1.1.1.1.1.1.2" xref="A1.17.17.17.1.m1.1.1.1.1.1.2.cmml">ν</mi><mo id="A1.17.17.17.1.m1.1.1.1.1.1.1" xref="A1.17.17.17.1.m1.1.1.1.1.1.1.cmml">=</mo><mn id="A1.17.17.17.1.m1.1.1.1.1.1.3" xref="A1.17.17.17.1.m1.1.1.1.1.1.3.cmml">0</mn></mrow><mo id="A1.17.17.17.1.m1.1.1.1.1.3" stretchy="false" xref="A1.17.17.17.1.m1.1.1.1.1.1.cmml">)</mo></mrow><mo id="A1.17.17.17.1.m1.2.2.3" xref="A1.17.17.17.1.m1.2.2.3.cmml">∨</mo><mrow id="A1.17.17.17.1.m1.2.2.2.1" xref="A1.17.17.17.1.m1.2.2.2.1.1.cmml"><mo id="A1.17.17.17.1.m1.2.2.2.1.2" stretchy="false" xref="A1.17.17.17.1.m1.2.2.2.1.1.cmml">(</mo><mrow id="A1.17.17.17.1.m1.2.2.2.1.1" xref="A1.17.17.17.1.m1.2.2.2.1.1.cmml"><mi id="A1.17.17.17.1.m1.2.2.2.1.1.2" xref="A1.17.17.17.1.m1.2.2.2.1.1.2.cmml">ν</mi><mo id="A1.17.17.17.1.m1.2.2.2.1.1.1" xref="A1.17.17.17.1.m1.2.2.2.1.1.1.cmml">=</mo><mrow id="A1.17.17.17.1.m1.2.2.2.1.1.3" xref="A1.17.17.17.1.m1.2.2.2.1.1.3.cmml"><mi id="A1.17.17.17.1.m1.2.2.2.1.1.3.2" xref="A1.17.17.17.1.m1.2.2.2.1.1.3.2.cmml">τ</mi><mo id="A1.17.17.17.1.m1.2.2.2.1.1.3.1" xref="A1.17.17.17.1.m1.2.2.2.1.1.3.1.cmml">+</mo><mn id="A1.17.17.17.1.m1.2.2.2.1.1.3.3" xref="A1.17.17.17.1.m1.2.2.2.1.1.3.3.cmml">1</mn><mo id="A1.17.17.17.1.m1.2.2.2.1.1.3.1a" xref="A1.17.17.17.1.m1.2.2.2.1.1.3.1.cmml">+</mo><mi id="A1.17.17.17.1.m1.2.2.2.1.1.3.4" xref="A1.17.17.17.1.m1.2.2.2.1.1.3.4.cmml">s</mi></mrow></mrow><mo id="A1.17.17.17.1.m1.2.2.2.1.3" stretchy="false" xref="A1.17.17.17.1.m1.2.2.2.1.1.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="A1.17.17.17.1.m1.2b"><apply id="A1.17.17.17.1.m1.2.2.cmml" xref="A1.17.17.17.1.m1.2.2"><or id="A1.17.17.17.1.m1.2.2.3.cmml" xref="A1.17.17.17.1.m1.2.2.3"></or><apply id="A1.17.17.17.1.m1.1.1.1.1.1.cmml" xref="A1.17.17.17.1.m1.1.1.1.1"><eq id="A1.17.17.17.1.m1.1.1.1.1.1.1.cmml" xref="A1.17.17.17.1.m1.1.1.1.1.1.1"></eq><ci id="A1.17.17.17.1.m1.1.1.1.1.1.2.cmml" xref="A1.17.17.17.1.m1.1.1.1.1.1.2">𝜈</ci><cn id="A1.17.17.17.1.m1.1.1.1.1.1.3.cmml" type="integer" xref="A1.17.17.17.1.m1.1.1.1.1.1.3">0</cn></apply><apply id="A1.17.17.17.1.m1.2.2.2.1.1.cmml" xref="A1.17.17.17.1.m1.2.2.2.1"><eq id="A1.17.17.17.1.m1.2.2.2.1.1.1.cmml" xref="A1.17.17.17.1.m1.2.2.2.1.1.1"></eq><ci id="A1.17.17.17.1.m1.2.2.2.1.1.2.cmml" xref="A1.17.17.17.1.m1.2.2.2.1.1.2">𝜈</ci><apply id="A1.17.17.17.1.m1.2.2.2.1.1.3.cmml" xref="A1.17.17.17.1.m1.2.2.2.1.1.3"><plus id="A1.17.17.17.1.m1.2.2.2.1.1.3.1.cmml" xref="A1.17.17.17.1.m1.2.2.2.1.1.3.1"></plus><ci id="A1.17.17.17.1.m1.2.2.2.1.1.3.2.cmml" xref="A1.17.17.17.1.m1.2.2.2.1.1.3.2">𝜏</ci><cn id="A1.17.17.17.1.m1.2.2.2.1.1.3.3.cmml" type="integer" xref="A1.17.17.17.1.m1.2.2.2.1.1.3.3">1</cn><ci id="A1.17.17.17.1.m1.2.2.2.1.1.3.4.cmml" xref="A1.17.17.17.1.m1.2.2.2.1.1.3.4">𝑠</ci></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.17.17.17.1.m1.2c">(\nu=0)\lor(\nu=\tau+1+s)</annotation><annotation encoding="application/x-llamapun" id="A1.17.17.17.1.m1.2d">( italic_ν = 0 ) ∨ ( italic_ν = italic_τ + 1 + italic_s )</annotation></semantics></math> then </div> <div class="ltx_listingline" id="A1.18.18.18"> for <math alttext="j\in\textup{a}" class="ltx_Math" display="inline" id="A1.18.18.18.1.m1.1"><semantics id="A1.18.18.18.1.m1.1a"><mrow id="A1.18.18.18.1.m1.1.1" xref="A1.18.18.18.1.m1.1.1.cmml"><mi id="A1.18.18.18.1.m1.1.1.2" xref="A1.18.18.18.1.m1.1.1.2.cmml">j</mi><mo id="A1.18.18.18.1.m1.1.1.1" xref="A1.18.18.18.1.m1.1.1.1.cmml">∈</mo><mtext id="A1.18.18.18.1.m1.1.1.3" xref="A1.18.18.18.1.m1.1.1.3b.cmml">a</mtext></mrow><annotation-xml encoding="MathML-Content" id="A1.18.18.18.1.m1.1b"><apply id="A1.18.18.18.1.m1.1.1.cmml" xref="A1.18.18.18.1.m1.1.1"><in id="A1.18.18.18.1.m1.1.1.1.cmml" xref="A1.18.18.18.1.m1.1.1.1"></in><ci id="A1.18.18.18.1.m1.1.1.2.cmml" xref="A1.18.18.18.1.m1.1.1.2">𝑗</ci><ci id="A1.18.18.18.1.m1.1.1.3b.cmml" xref="A1.18.18.18.1.m1.1.1.3"><mtext id="A1.18.18.18.1.m1.1.1.3.cmml" xref="A1.18.18.18.1.m1.1.1.3">a</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.18.18.18.1.m1.1c">j\in\textup{a}</annotation><annotation encoding="application/x-llamapun" id="A1.18.18.18.1.m1.1d">italic_j ∈ a</annotation></semantics></math> do </div> <div class="ltx_listingline" id="A1.19.19.19"> if <math alttext="\boldsymbol{M}_{i,j}=1" class="ltx_Math" display="inline" id="A1.19.19.19.1.m1.2"><semantics id="A1.19.19.19.1.m1.2a"><mrow id="A1.19.19.19.1.m1.2.3" xref="A1.19.19.19.1.m1.2.3.cmml"><msub id="A1.19.19.19.1.m1.2.3.2" xref="A1.19.19.19.1.m1.2.3.2.cmml"><mi id="A1.19.19.19.1.m1.2.3.2.2" xref="A1.19.19.19.1.m1.2.3.2.2.cmml">𝐌</mi><mrow id="A1.19.19.19.1.m1.2.2.2.4" xref="A1.19.19.19.1.m1.2.2.2.3.cmml"><mi id="A1.19.19.19.1.m1.1.1.1.1" xref="A1.19.19.19.1.m1.1.1.1.1.cmml">i</mi><mo id="A1.19.19.19.1.m1.2.2.2.4.1" xref="A1.19.19.19.1.m1.2.2.2.3.cmml">,</mo><mi id="A1.19.19.19.1.m1.2.2.2.2" xref="A1.19.19.19.1.m1.2.2.2.2.cmml">j</mi></mrow></msub><mo id="A1.19.19.19.1.m1.2.3.1" xref="A1.19.19.19.1.m1.2.3.1.cmml">=</mo><mn id="A1.19.19.19.1.m1.2.3.3" xref="A1.19.19.19.1.m1.2.3.3.cmml">1</mn></mrow><annotation-xml encoding="MathML-Content" id="A1.19.19.19.1.m1.2b"><apply id="A1.19.19.19.1.m1.2.3.cmml" xref="A1.19.19.19.1.m1.2.3"><eq id="A1.19.19.19.1.m1.2.3.1.cmml" xref="A1.19.19.19.1.m1.2.3.1"></eq><apply id="A1.19.19.19.1.m1.2.3.2.cmml" xref="A1.19.19.19.1.m1.2.3.2"><csymbol cd="ambiguous" id="A1.19.19.19.1.m1.2.3.2.1.cmml" xref="A1.19.19.19.1.m1.2.3.2">subscript</csymbol><ci id="A1.19.19.19.1.m1.2.3.2.2.cmml" xref="A1.19.19.19.1.m1.2.3.2.2">𝐌</ci><list id="A1.19.19.19.1.m1.2.2.2.3.cmml" xref="A1.19.19.19.1.m1.2.2.2.4"><ci id="A1.19.19.19.1.m1.1.1.1.1.cmml" xref="A1.19.19.19.1.m1.1.1.1.1">𝑖</ci><ci id="A1.19.19.19.1.m1.2.2.2.2.cmml" xref="A1.19.19.19.1.m1.2.2.2.2">𝑗</ci></list></apply><cn id="A1.19.19.19.1.m1.2.3.3.cmml" type="integer" xref="A1.19.19.19.1.m1.2.3.3">1</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.19.19.19.1.m1.2c">\boldsymbol{M}_{i,j}=1</annotation><annotation encoding="application/x-llamapun" id="A1.19.19.19.1.m1.2d">bold_italic_M start_POSTSUBSCRIPT italic_i , italic_j end_POSTSUBSCRIPT = 1</annotation></semantics></math> then </div> <div class="ltx_listingline" id="A1.20.20.20"> <math alttext="\delta\leftarrow\sqrt{(\tau-i)^{2}+(\tau-j)^{2}}" class="ltx_Math" display="inline" id="A1.20.20.20.m1.2"><semantics id="A1.20.20.20.m1.2a"><mrow id="A1.20.20.20.m1.2.3" xref="A1.20.20.20.m1.2.3.cmml"><mi id="A1.20.20.20.m1.2.3.2" xref="A1.20.20.20.m1.2.3.2.cmml">δ</mi><mo id="A1.20.20.20.m1.2.3.1" stretchy="false" xref="A1.20.20.20.m1.2.3.1.cmml">←</mo><msqrt id="A1.20.20.20.m1.2.2" xref="A1.20.20.20.m1.2.2.cmml"><mrow id="A1.20.20.20.m1.2.2.2" xref="A1.20.20.20.m1.2.2.2.cmml"><msup id="A1.20.20.20.m1.1.1.1.1" xref="A1.20.20.20.m1.1.1.1.1.cmml"><mrow id="A1.20.20.20.m1.1.1.1.1.1.1" xref="A1.20.20.20.m1.1.1.1.1.1.1.1.cmml"><mo id="A1.20.20.20.m1.1.1.1.1.1.1.2" stretchy="false" xref="A1.20.20.20.m1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="A1.20.20.20.m1.1.1.1.1.1.1.1" xref="A1.20.20.20.m1.1.1.1.1.1.1.1.cmml"><mi id="A1.20.20.20.m1.1.1.1.1.1.1.1.2" xref="A1.20.20.20.m1.1.1.1.1.1.1.1.2.cmml">τ</mi><mo id="A1.20.20.20.m1.1.1.1.1.1.1.1.1" xref="A1.20.20.20.m1.1.1.1.1.1.1.1.1.cmml">−</mo><mi id="A1.20.20.20.m1.1.1.1.1.1.1.1.3" xref="A1.20.20.20.m1.1.1.1.1.1.1.1.3.cmml">i</mi></mrow><mo id="A1.20.20.20.m1.1.1.1.1.1.1.3" stretchy="false" xref="A1.20.20.20.m1.1.1.1.1.1.1.1.cmml">)</mo></mrow><mn id="A1.20.20.20.m1.1.1.1.1.3" xref="A1.20.20.20.m1.1.1.1.1.3.cmml">2</mn></msup><mo id="A1.20.20.20.m1.2.2.2.3" xref="A1.20.20.20.m1.2.2.2.3.cmml">+</mo><msup id="A1.20.20.20.m1.2.2.2.2" xref="A1.20.20.20.m1.2.2.2.2.cmml"><mrow id="A1.20.20.20.m1.2.2.2.2.1.1" xref="A1.20.20.20.m1.2.2.2.2.1.1.1.cmml"><mo id="A1.20.20.20.m1.2.2.2.2.1.1.2" stretchy="false" xref="A1.20.20.20.m1.2.2.2.2.1.1.1.cmml">(</mo><mrow id="A1.20.20.20.m1.2.2.2.2.1.1.1" xref="A1.20.20.20.m1.2.2.2.2.1.1.1.cmml"><mi id="A1.20.20.20.m1.2.2.2.2.1.1.1.2" xref="A1.20.20.20.m1.2.2.2.2.1.1.1.2.cmml">τ</mi><mo id="A1.20.20.20.m1.2.2.2.2.1.1.1.1" xref="A1.20.20.20.m1.2.2.2.2.1.1.1.1.cmml">−</mo><mi id="A1.20.20.20.m1.2.2.2.2.1.1.1.3" xref="A1.20.20.20.m1.2.2.2.2.1.1.1.3.cmml">j</mi></mrow><mo id="A1.20.20.20.m1.2.2.2.2.1.1.3" stretchy="false" xref="A1.20.20.20.m1.2.2.2.2.1.1.1.cmml">)</mo></mrow><mn id="A1.20.20.20.m1.2.2.2.2.3" xref="A1.20.20.20.m1.2.2.2.2.3.cmml">2</mn></msup></mrow></msqrt></mrow><annotation-xml encoding="MathML-Content" id="A1.20.20.20.m1.2b"><apply id="A1.20.20.20.m1.2.3.cmml" xref="A1.20.20.20.m1.2.3"><ci id="A1.20.20.20.m1.2.3.1.cmml" xref="A1.20.20.20.m1.2.3.1">←</ci><ci id="A1.20.20.20.m1.2.3.2.cmml" xref="A1.20.20.20.m1.2.3.2">𝛿</ci><apply id="A1.20.20.20.m1.2.2.cmml" xref="A1.20.20.20.m1.2.2"><root id="A1.20.20.20.m1.2.2a.cmml" xref="A1.20.20.20.m1.2.2"></root><apply id="A1.20.20.20.m1.2.2.2.cmml" xref="A1.20.20.20.m1.2.2.2"><plus id="A1.20.20.20.m1.2.2.2.3.cmml" xref="A1.20.20.20.m1.2.2.2.3"></plus><apply id="A1.20.20.20.m1.1.1.1.1.cmml" xref="A1.20.20.20.m1.1.1.1.1"><csymbol cd="ambiguous" id="A1.20.20.20.m1.1.1.1.1.2.cmml" xref="A1.20.20.20.m1.1.1.1.1">superscript</csymbol><apply id="A1.20.20.20.m1.1.1.1.1.1.1.1.cmml" xref="A1.20.20.20.m1.1.1.1.1.1.1"><minus id="A1.20.20.20.m1.1.1.1.1.1.1.1.1.cmml" xref="A1.20.20.20.m1.1.1.1.1.1.1.1.1"></minus><ci id="A1.20.20.20.m1.1.1.1.1.1.1.1.2.cmml" xref="A1.20.20.20.m1.1.1.1.1.1.1.1.2">𝜏</ci><ci id="A1.20.20.20.m1.1.1.1.1.1.1.1.3.cmml" xref="A1.20.20.20.m1.1.1.1.1.1.1.1.3">𝑖</ci></apply><cn id="A1.20.20.20.m1.1.1.1.1.3.cmml" type="integer" xref="A1.20.20.20.m1.1.1.1.1.3">2</cn></apply><apply id="A1.20.20.20.m1.2.2.2.2.cmml" xref="A1.20.20.20.m1.2.2.2.2"><csymbol cd="ambiguous" id="A1.20.20.20.m1.2.2.2.2.2.cmml" xref="A1.20.20.20.m1.2.2.2.2">superscript</csymbol><apply id="A1.20.20.20.m1.2.2.2.2.1.1.1.cmml" xref="A1.20.20.20.m1.2.2.2.2.1.1"><minus id="A1.20.20.20.m1.2.2.2.2.1.1.1.1.cmml" xref="A1.20.20.20.m1.2.2.2.2.1.1.1.1"></minus><ci id="A1.20.20.20.m1.2.2.2.2.1.1.1.2.cmml" xref="A1.20.20.20.m1.2.2.2.2.1.1.1.2">𝜏</ci><ci id="A1.20.20.20.m1.2.2.2.2.1.1.1.3.cmml" xref="A1.20.20.20.m1.2.2.2.2.1.1.1.3">𝑗</ci></apply><cn id="A1.20.20.20.m1.2.2.2.2.3.cmml" type="integer" xref="A1.20.20.20.m1.2.2.2.2.3">2</cn></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.20.20.20.m1.2c">\delta\leftarrow\sqrt{(\tau-i)^{2}+(\tau-j)^{2}}</annotation><annotation encoding="application/x-llamapun" id="A1.20.20.20.m1.2d">italic_δ ← square-root start_ARG ( italic_τ - italic_i ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + ( italic_τ - italic_j ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.21.21.21"> <math alttext="x_{1},x_{2},f\leftarrow i,j,\textup{False}" class="ltx_Math" display="inline" id="A1.21.21.21.m1.5"><semantics id="A1.21.21.21.m1.5a"><mrow id="A1.21.21.21.m1.5.5.2" xref="A1.21.21.21.m1.5.5.3.cmml"><mrow id="A1.21.21.21.m1.4.4.1.1" xref="A1.21.21.21.m1.4.4.1.1.cmml"><mrow id="A1.21.21.21.m1.4.4.1.1.2.2" xref="A1.21.21.21.m1.4.4.1.1.2.3.cmml"><msub id="A1.21.21.21.m1.4.4.1.1.1.1.1" xref="A1.21.21.21.m1.4.4.1.1.1.1.1.cmml"><mi id="A1.21.21.21.m1.4.4.1.1.1.1.1.2" xref="A1.21.21.21.m1.4.4.1.1.1.1.1.2.cmml">x</mi><mn id="A1.21.21.21.m1.4.4.1.1.1.1.1.3" xref="A1.21.21.21.m1.4.4.1.1.1.1.1.3.cmml">1</mn></msub><mo id="A1.21.21.21.m1.4.4.1.1.2.2.3" xref="A1.21.21.21.m1.4.4.1.1.2.3.cmml">,</mo><msub id="A1.21.21.21.m1.4.4.1.1.2.2.2" xref="A1.21.21.21.m1.4.4.1.1.2.2.2.cmml"><mi id="A1.21.21.21.m1.4.4.1.1.2.2.2.2" xref="A1.21.21.21.m1.4.4.1.1.2.2.2.2.cmml">x</mi><mn id="A1.21.21.21.m1.4.4.1.1.2.2.2.3" xref="A1.21.21.21.m1.4.4.1.1.2.2.2.3.cmml">2</mn></msub><mo id="A1.21.21.21.m1.4.4.1.1.2.2.4" xref="A1.21.21.21.m1.4.4.1.1.2.3.cmml">,</mo><mi id="A1.21.21.21.m1.1.1" xref="A1.21.21.21.m1.1.1.cmml">f</mi></mrow><mo id="A1.21.21.21.m1.4.4.1.1.3" stretchy="false" xref="A1.21.21.21.m1.4.4.1.1.3.cmml">←</mo><mi id="A1.21.21.21.m1.4.4.1.1.4" xref="A1.21.21.21.m1.4.4.1.1.4.cmml">i</mi></mrow><mo id="A1.21.21.21.m1.5.5.2.3" xref="A1.21.21.21.m1.5.5.3a.cmml">,</mo><mrow id="A1.21.21.21.m1.5.5.2.2.2" xref="A1.21.21.21.m1.5.5.2.2.1.cmml"><mi id="A1.21.21.21.m1.2.2" xref="A1.21.21.21.m1.2.2.cmml">j</mi><mo id="A1.21.21.21.m1.5.5.2.2.2.1" xref="A1.21.21.21.m1.5.5.2.2.1.cmml">,</mo><mtext id="A1.21.21.21.m1.3.3" xref="A1.21.21.21.m1.3.3a.cmml">False</mtext></mrow></mrow><annotation-xml encoding="MathML-Content" id="A1.21.21.21.m1.5b"><apply id="A1.21.21.21.m1.5.5.3.cmml" xref="A1.21.21.21.m1.5.5.2"><csymbol cd="ambiguous" id="A1.21.21.21.m1.5.5.3a.cmml" xref="A1.21.21.21.m1.5.5.2.3">formulae-sequence</csymbol><apply id="A1.21.21.21.m1.4.4.1.1.cmml" xref="A1.21.21.21.m1.4.4.1.1"><ci id="A1.21.21.21.m1.4.4.1.1.3.cmml" xref="A1.21.21.21.m1.4.4.1.1.3">←</ci><list id="A1.21.21.21.m1.4.4.1.1.2.3.cmml" xref="A1.21.21.21.m1.4.4.1.1.2.2"><apply id="A1.21.21.21.m1.4.4.1.1.1.1.1.cmml" xref="A1.21.21.21.m1.4.4.1.1.1.1.1"><csymbol cd="ambiguous" id="A1.21.21.21.m1.4.4.1.1.1.1.1.1.cmml" xref="A1.21.21.21.m1.4.4.1.1.1.1.1">subscript</csymbol><ci id="A1.21.21.21.m1.4.4.1.1.1.1.1.2.cmml" xref="A1.21.21.21.m1.4.4.1.1.1.1.1.2">𝑥</ci><cn id="A1.21.21.21.m1.4.4.1.1.1.1.1.3.cmml" type="integer" xref="A1.21.21.21.m1.4.4.1.1.1.1.1.3">1</cn></apply><apply id="A1.21.21.21.m1.4.4.1.1.2.2.2.cmml" xref="A1.21.21.21.m1.4.4.1.1.2.2.2"><csymbol cd="ambiguous" id="A1.21.21.21.m1.4.4.1.1.2.2.2.1.cmml" xref="A1.21.21.21.m1.4.4.1.1.2.2.2">subscript</csymbol><ci id="A1.21.21.21.m1.4.4.1.1.2.2.2.2.cmml" xref="A1.21.21.21.m1.4.4.1.1.2.2.2.2">𝑥</ci><cn id="A1.21.21.21.m1.4.4.1.1.2.2.2.3.cmml" type="integer" xref="A1.21.21.21.m1.4.4.1.1.2.2.2.3">2</cn></apply><ci id="A1.21.21.21.m1.1.1.cmml" xref="A1.21.21.21.m1.1.1">𝑓</ci></list><ci id="A1.21.21.21.m1.4.4.1.1.4.cmml" xref="A1.21.21.21.m1.4.4.1.1.4">𝑖</ci></apply><list id="A1.21.21.21.m1.5.5.2.2.1.cmml" xref="A1.21.21.21.m1.5.5.2.2.2"><ci id="A1.21.21.21.m1.2.2.cmml" xref="A1.21.21.21.m1.2.2">𝑗</ci><ci id="A1.21.21.21.m1.3.3a.cmml" xref="A1.21.21.21.m1.3.3"><mtext id="A1.21.21.21.m1.3.3.cmml" xref="A1.21.21.21.m1.3.3">False</mtext></ci></list></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.21.21.21.m1.5c">x_{1},x_{2},f\leftarrow i,j,\textup{False}</annotation><annotation encoding="application/x-llamapun" id="A1.21.21.21.m1.5d">italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , italic_f ← italic_i , italic_j , False</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.22.22.22"> return <math alttext="x_{1},x_{2},\delta,f" class="ltx_Math" display="inline" id="A1.22.22.22.m1.4"><semantics id="A1.22.22.22.m1.4a"><mrow id="A1.22.22.22.m1.4.4.2" xref="A1.22.22.22.m1.4.4.3.cmml"><msub id="A1.22.22.22.m1.3.3.1.1" xref="A1.22.22.22.m1.3.3.1.1.cmml"><mi id="A1.22.22.22.m1.3.3.1.1.2" xref="A1.22.22.22.m1.3.3.1.1.2.cmml">x</mi><mn id="A1.22.22.22.m1.3.3.1.1.3" xref="A1.22.22.22.m1.3.3.1.1.3.cmml">1</mn></msub><mo id="A1.22.22.22.m1.4.4.2.3" xref="A1.22.22.22.m1.4.4.3.cmml">,</mo><msub id="A1.22.22.22.m1.4.4.2.2" xref="A1.22.22.22.m1.4.4.2.2.cmml"><mi id="A1.22.22.22.m1.4.4.2.2.2" xref="A1.22.22.22.m1.4.4.2.2.2.cmml">x</mi><mn id="A1.22.22.22.m1.4.4.2.2.3" xref="A1.22.22.22.m1.4.4.2.2.3.cmml">2</mn></msub><mo id="A1.22.22.22.m1.4.4.2.4" xref="A1.22.22.22.m1.4.4.3.cmml">,</mo><mi id="A1.22.22.22.m1.1.1" xref="A1.22.22.22.m1.1.1.cmml">δ</mi><mo id="A1.22.22.22.m1.4.4.2.5" xref="A1.22.22.22.m1.4.4.3.cmml">,</mo><mi id="A1.22.22.22.m1.2.2" xref="A1.22.22.22.m1.2.2.cmml">f</mi></mrow><annotation-xml encoding="MathML-Content" id="A1.22.22.22.m1.4b"><list id="A1.22.22.22.m1.4.4.3.cmml" xref="A1.22.22.22.m1.4.4.2"><apply id="A1.22.22.22.m1.3.3.1.1.cmml" xref="A1.22.22.22.m1.3.3.1.1"><csymbol cd="ambiguous" id="A1.22.22.22.m1.3.3.1.1.1.cmml" xref="A1.22.22.22.m1.3.3.1.1">subscript</csymbol><ci id="A1.22.22.22.m1.3.3.1.1.2.cmml" xref="A1.22.22.22.m1.3.3.1.1.2">𝑥</ci><cn id="A1.22.22.22.m1.3.3.1.1.3.cmml" type="integer" xref="A1.22.22.22.m1.3.3.1.1.3">1</cn></apply><apply id="A1.22.22.22.m1.4.4.2.2.cmml" xref="A1.22.22.22.m1.4.4.2.2"><csymbol cd="ambiguous" id="A1.22.22.22.m1.4.4.2.2.1.cmml" xref="A1.22.22.22.m1.4.4.2.2">subscript</csymbol><ci id="A1.22.22.22.m1.4.4.2.2.2.cmml" xref="A1.22.22.22.m1.4.4.2.2.2">𝑥</ci><cn id="A1.22.22.22.m1.4.4.2.2.3.cmml" type="integer" xref="A1.22.22.22.m1.4.4.2.2.3">2</cn></apply><ci id="A1.22.22.22.m1.1.1.cmml" xref="A1.22.22.22.m1.1.1">𝛿</ci><ci id="A1.22.22.22.m1.2.2.cmml" xref="A1.22.22.22.m1.2.2">𝑓</ci></list></annotation-xml><annotation encoding="application/x-tex" id="A1.22.22.22.m1.4c">x_{1},x_{2},\delta,f</annotation><annotation encoding="application/x-llamapun" id="A1.22.22.22.m1.4d">italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , italic_δ , italic_f</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.29.29.31"> end for </div> <div class="ltx_listingline" id="A1.29.29.32"> </div> <div class="ltx_listingline" id="A1.29.29.33"> else </div> <div class="ltx_listingline" id="A1.23.23.23"> for <math alttext="j\in\{\boldsymbol{a}_{0},\boldsymbol{a}_{|a|}\}" class="ltx_Math" display="inline" id="A1.23.23.23.1.m1.3"><semantics id="A1.23.23.23.1.m1.3a"><mrow id="A1.23.23.23.1.m1.3.3" xref="A1.23.23.23.1.m1.3.3.cmml"><mi id="A1.23.23.23.1.m1.3.3.4" xref="A1.23.23.23.1.m1.3.3.4.cmml">j</mi><mo id="A1.23.23.23.1.m1.3.3.3" xref="A1.23.23.23.1.m1.3.3.3.cmml">∈</mo><mrow id="A1.23.23.23.1.m1.3.3.2.2" xref="A1.23.23.23.1.m1.3.3.2.3.cmml"><mo id="A1.23.23.23.1.m1.3.3.2.2.3" stretchy="false" xref="A1.23.23.23.1.m1.3.3.2.3.cmml">{</mo><msub id="A1.23.23.23.1.m1.2.2.1.1.1" xref="A1.23.23.23.1.m1.2.2.1.1.1.cmml"><mi id="A1.23.23.23.1.m1.2.2.1.1.1.2" xref="A1.23.23.23.1.m1.2.2.1.1.1.2.cmml">𝐚</mi><mn id="A1.23.23.23.1.m1.2.2.1.1.1.3" xref="A1.23.23.23.1.m1.2.2.1.1.1.3.cmml">0</mn></msub><mo id="A1.23.23.23.1.m1.3.3.2.2.4" xref="A1.23.23.23.1.m1.3.3.2.3.cmml">,</mo><msub id="A1.23.23.23.1.m1.3.3.2.2.2" xref="A1.23.23.23.1.m1.3.3.2.2.2.cmml"><mi id="A1.23.23.23.1.m1.3.3.2.2.2.2" xref="A1.23.23.23.1.m1.3.3.2.2.2.2.cmml">𝐚</mi><mrow id="A1.23.23.23.1.m1.1.1.1.3" xref="A1.23.23.23.1.m1.1.1.1.2.cmml"><mo id="A1.23.23.23.1.m1.1.1.1.3.1" stretchy="false" xref="A1.23.23.23.1.m1.1.1.1.2.1.cmml">|</mo><mi id="A1.23.23.23.1.m1.1.1.1.1" xref="A1.23.23.23.1.m1.1.1.1.1.cmml">a</mi><mo id="A1.23.23.23.1.m1.1.1.1.3.2" stretchy="false" xref="A1.23.23.23.1.m1.1.1.1.2.1.cmml">|</mo></mrow></msub><mo id="A1.23.23.23.1.m1.3.3.2.2.5" stretchy="false" xref="A1.23.23.23.1.m1.3.3.2.3.cmml">}</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="A1.23.23.23.1.m1.3b"><apply id="A1.23.23.23.1.m1.3.3.cmml" xref="A1.23.23.23.1.m1.3.3"><in id="A1.23.23.23.1.m1.3.3.3.cmml" xref="A1.23.23.23.1.m1.3.3.3"></in><ci id="A1.23.23.23.1.m1.3.3.4.cmml" xref="A1.23.23.23.1.m1.3.3.4">𝑗</ci><set id="A1.23.23.23.1.m1.3.3.2.3.cmml" xref="A1.23.23.23.1.m1.3.3.2.2"><apply id="A1.23.23.23.1.m1.2.2.1.1.1.cmml" xref="A1.23.23.23.1.m1.2.2.1.1.1"><csymbol cd="ambiguous" id="A1.23.23.23.1.m1.2.2.1.1.1.1.cmml" xref="A1.23.23.23.1.m1.2.2.1.1.1">subscript</csymbol><ci id="A1.23.23.23.1.m1.2.2.1.1.1.2.cmml" xref="A1.23.23.23.1.m1.2.2.1.1.1.2">𝐚</ci><cn id="A1.23.23.23.1.m1.2.2.1.1.1.3.cmml" type="integer" xref="A1.23.23.23.1.m1.2.2.1.1.1.3">0</cn></apply><apply id="A1.23.23.23.1.m1.3.3.2.2.2.cmml" xref="A1.23.23.23.1.m1.3.3.2.2.2"><csymbol cd="ambiguous" id="A1.23.23.23.1.m1.3.3.2.2.2.1.cmml" xref="A1.23.23.23.1.m1.3.3.2.2.2">subscript</csymbol><ci id="A1.23.23.23.1.m1.3.3.2.2.2.2.cmml" xref="A1.23.23.23.1.m1.3.3.2.2.2.2">𝐚</ci><apply id="A1.23.23.23.1.m1.1.1.1.2.cmml" xref="A1.23.23.23.1.m1.1.1.1.3"><abs id="A1.23.23.23.1.m1.1.1.1.2.1.cmml" xref="A1.23.23.23.1.m1.1.1.1.3.1"></abs><ci id="A1.23.23.23.1.m1.1.1.1.1.cmml" xref="A1.23.23.23.1.m1.1.1.1.1">𝑎</ci></apply></apply></set></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.23.23.23.1.m1.3c">j\in\{\boldsymbol{a}_{0},\boldsymbol{a}_{|a|}\}</annotation><annotation encoding="application/x-llamapun" id="A1.23.23.23.1.m1.3d">italic_j ∈ { bold_italic_a start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , bold_italic_a start_POSTSUBSCRIPT | italic_a | end_POSTSUBSCRIPT }</annotation></semantics></math> do </div> <div class="ltx_listingline" id="A1.24.24.24"> if <math alttext="\boldsymbol{M}_{i,j}=1" class="ltx_Math" display="inline" id="A1.24.24.24.1.m1.2"><semantics id="A1.24.24.24.1.m1.2a"><mrow id="A1.24.24.24.1.m1.2.3" xref="A1.24.24.24.1.m1.2.3.cmml"><msub id="A1.24.24.24.1.m1.2.3.2" xref="A1.24.24.24.1.m1.2.3.2.cmml"><mi id="A1.24.24.24.1.m1.2.3.2.2" xref="A1.24.24.24.1.m1.2.3.2.2.cmml">𝐌</mi><mrow id="A1.24.24.24.1.m1.2.2.2.4" xref="A1.24.24.24.1.m1.2.2.2.3.cmml"><mi id="A1.24.24.24.1.m1.1.1.1.1" xref="A1.24.24.24.1.m1.1.1.1.1.cmml">i</mi><mo id="A1.24.24.24.1.m1.2.2.2.4.1" xref="A1.24.24.24.1.m1.2.2.2.3.cmml">,</mo><mi id="A1.24.24.24.1.m1.2.2.2.2" xref="A1.24.24.24.1.m1.2.2.2.2.cmml">j</mi></mrow></msub><mo id="A1.24.24.24.1.m1.2.3.1" xref="A1.24.24.24.1.m1.2.3.1.cmml">=</mo><mn id="A1.24.24.24.1.m1.2.3.3" xref="A1.24.24.24.1.m1.2.3.3.cmml">1</mn></mrow><annotation-xml encoding="MathML-Content" id="A1.24.24.24.1.m1.2b"><apply id="A1.24.24.24.1.m1.2.3.cmml" xref="A1.24.24.24.1.m1.2.3"><eq id="A1.24.24.24.1.m1.2.3.1.cmml" xref="A1.24.24.24.1.m1.2.3.1"></eq><apply id="A1.24.24.24.1.m1.2.3.2.cmml" xref="A1.24.24.24.1.m1.2.3.2"><csymbol cd="ambiguous" id="A1.24.24.24.1.m1.2.3.2.1.cmml" xref="A1.24.24.24.1.m1.2.3.2">subscript</csymbol><ci id="A1.24.24.24.1.m1.2.3.2.2.cmml" xref="A1.24.24.24.1.m1.2.3.2.2">𝐌</ci><list id="A1.24.24.24.1.m1.2.2.2.3.cmml" xref="A1.24.24.24.1.m1.2.2.2.4"><ci id="A1.24.24.24.1.m1.1.1.1.1.cmml" xref="A1.24.24.24.1.m1.1.1.1.1">𝑖</ci><ci id="A1.24.24.24.1.m1.2.2.2.2.cmml" xref="A1.24.24.24.1.m1.2.2.2.2">𝑗</ci></list></apply><cn id="A1.24.24.24.1.m1.2.3.3.cmml" type="integer" xref="A1.24.24.24.1.m1.2.3.3">1</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.24.24.24.1.m1.2c">\boldsymbol{M}_{i,j}=1</annotation><annotation encoding="application/x-llamapun" id="A1.24.24.24.1.m1.2d">bold_italic_M start_POSTSUBSCRIPT italic_i , italic_j end_POSTSUBSCRIPT = 1</annotation></semantics></math> then </div> <div class="ltx_listingline" id="A1.25.25.25"> <math alttext="\delta\leftarrow\sqrt{(\tau-i)^{2}+(\tau-j)^{2}}" class="ltx_Math" display="inline" id="A1.25.25.25.m1.2"><semantics id="A1.25.25.25.m1.2a"><mrow id="A1.25.25.25.m1.2.3" xref="A1.25.25.25.m1.2.3.cmml"><mi id="A1.25.25.25.m1.2.3.2" xref="A1.25.25.25.m1.2.3.2.cmml">δ</mi><mo id="A1.25.25.25.m1.2.3.1" stretchy="false" xref="A1.25.25.25.m1.2.3.1.cmml">←</mo><msqrt id="A1.25.25.25.m1.2.2" xref="A1.25.25.25.m1.2.2.cmml"><mrow id="A1.25.25.25.m1.2.2.2" xref="A1.25.25.25.m1.2.2.2.cmml"><msup id="A1.25.25.25.m1.1.1.1.1" xref="A1.25.25.25.m1.1.1.1.1.cmml"><mrow id="A1.25.25.25.m1.1.1.1.1.1.1" xref="A1.25.25.25.m1.1.1.1.1.1.1.1.cmml"><mo id="A1.25.25.25.m1.1.1.1.1.1.1.2" stretchy="false" xref="A1.25.25.25.m1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="A1.25.25.25.m1.1.1.1.1.1.1.1" xref="A1.25.25.25.m1.1.1.1.1.1.1.1.cmml"><mi id="A1.25.25.25.m1.1.1.1.1.1.1.1.2" xref="A1.25.25.25.m1.1.1.1.1.1.1.1.2.cmml">τ</mi><mo id="A1.25.25.25.m1.1.1.1.1.1.1.1.1" xref="A1.25.25.25.m1.1.1.1.1.1.1.1.1.cmml">−</mo><mi id="A1.25.25.25.m1.1.1.1.1.1.1.1.3" xref="A1.25.25.25.m1.1.1.1.1.1.1.1.3.cmml">i</mi></mrow><mo id="A1.25.25.25.m1.1.1.1.1.1.1.3" stretchy="false" xref="A1.25.25.25.m1.1.1.1.1.1.1.1.cmml">)</mo></mrow><mn id="A1.25.25.25.m1.1.1.1.1.3" xref="A1.25.25.25.m1.1.1.1.1.3.cmml">2</mn></msup><mo id="A1.25.25.25.m1.2.2.2.3" xref="A1.25.25.25.m1.2.2.2.3.cmml">+</mo><msup id="A1.25.25.25.m1.2.2.2.2" xref="A1.25.25.25.m1.2.2.2.2.cmml"><mrow id="A1.25.25.25.m1.2.2.2.2.1.1" xref="A1.25.25.25.m1.2.2.2.2.1.1.1.cmml"><mo id="A1.25.25.25.m1.2.2.2.2.1.1.2" stretchy="false" xref="A1.25.25.25.m1.2.2.2.2.1.1.1.cmml">(</mo><mrow id="A1.25.25.25.m1.2.2.2.2.1.1.1" xref="A1.25.25.25.m1.2.2.2.2.1.1.1.cmml"><mi id="A1.25.25.25.m1.2.2.2.2.1.1.1.2" xref="A1.25.25.25.m1.2.2.2.2.1.1.1.2.cmml">τ</mi><mo id="A1.25.25.25.m1.2.2.2.2.1.1.1.1" xref="A1.25.25.25.m1.2.2.2.2.1.1.1.1.cmml">−</mo><mi id="A1.25.25.25.m1.2.2.2.2.1.1.1.3" xref="A1.25.25.25.m1.2.2.2.2.1.1.1.3.cmml">j</mi></mrow><mo id="A1.25.25.25.m1.2.2.2.2.1.1.3" stretchy="false" xref="A1.25.25.25.m1.2.2.2.2.1.1.1.cmml">)</mo></mrow><mn id="A1.25.25.25.m1.2.2.2.2.3" xref="A1.25.25.25.m1.2.2.2.2.3.cmml">2</mn></msup></mrow></msqrt></mrow><annotation-xml encoding="MathML-Content" id="A1.25.25.25.m1.2b"><apply id="A1.25.25.25.m1.2.3.cmml" xref="A1.25.25.25.m1.2.3"><ci id="A1.25.25.25.m1.2.3.1.cmml" xref="A1.25.25.25.m1.2.3.1">←</ci><ci id="A1.25.25.25.m1.2.3.2.cmml" xref="A1.25.25.25.m1.2.3.2">𝛿</ci><apply id="A1.25.25.25.m1.2.2.cmml" xref="A1.25.25.25.m1.2.2"><root id="A1.25.25.25.m1.2.2a.cmml" xref="A1.25.25.25.m1.2.2"></root><apply id="A1.25.25.25.m1.2.2.2.cmml" xref="A1.25.25.25.m1.2.2.2"><plus id="A1.25.25.25.m1.2.2.2.3.cmml" xref="A1.25.25.25.m1.2.2.2.3"></plus><apply id="A1.25.25.25.m1.1.1.1.1.cmml" xref="A1.25.25.25.m1.1.1.1.1"><csymbol cd="ambiguous" id="A1.25.25.25.m1.1.1.1.1.2.cmml" xref="A1.25.25.25.m1.1.1.1.1">superscript</csymbol><apply id="A1.25.25.25.m1.1.1.1.1.1.1.1.cmml" xref="A1.25.25.25.m1.1.1.1.1.1.1"><minus id="A1.25.25.25.m1.1.1.1.1.1.1.1.1.cmml" xref="A1.25.25.25.m1.1.1.1.1.1.1.1.1"></minus><ci id="A1.25.25.25.m1.1.1.1.1.1.1.1.2.cmml" xref="A1.25.25.25.m1.1.1.1.1.1.1.1.2">𝜏</ci><ci id="A1.25.25.25.m1.1.1.1.1.1.1.1.3.cmml" xref="A1.25.25.25.m1.1.1.1.1.1.1.1.3">𝑖</ci></apply><cn id="A1.25.25.25.m1.1.1.1.1.3.cmml" type="integer" xref="A1.25.25.25.m1.1.1.1.1.3">2</cn></apply><apply id="A1.25.25.25.m1.2.2.2.2.cmml" xref="A1.25.25.25.m1.2.2.2.2"><csymbol cd="ambiguous" id="A1.25.25.25.m1.2.2.2.2.2.cmml" xref="A1.25.25.25.m1.2.2.2.2">superscript</csymbol><apply id="A1.25.25.25.m1.2.2.2.2.1.1.1.cmml" xref="A1.25.25.25.m1.2.2.2.2.1.1"><minus id="A1.25.25.25.m1.2.2.2.2.1.1.1.1.cmml" xref="A1.25.25.25.m1.2.2.2.2.1.1.1.1"></minus><ci id="A1.25.25.25.m1.2.2.2.2.1.1.1.2.cmml" xref="A1.25.25.25.m1.2.2.2.2.1.1.1.2">𝜏</ci><ci id="A1.25.25.25.m1.2.2.2.2.1.1.1.3.cmml" xref="A1.25.25.25.m1.2.2.2.2.1.1.1.3">𝑗</ci></apply><cn id="A1.25.25.25.m1.2.2.2.2.3.cmml" type="integer" xref="A1.25.25.25.m1.2.2.2.2.3">2</cn></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.25.25.25.m1.2c">\delta\leftarrow\sqrt{(\tau-i)^{2}+(\tau-j)^{2}}</annotation><annotation encoding="application/x-llamapun" id="A1.25.25.25.m1.2d">italic_δ ← square-root start_ARG ( italic_τ - italic_i ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + ( italic_τ - italic_j ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.26.26.26"> <math alttext="x_{1},x_{2},f\leftarrow i,j,\textup{False}" class="ltx_Math" display="inline" id="A1.26.26.26.m1.5"><semantics id="A1.26.26.26.m1.5a"><mrow id="A1.26.26.26.m1.5.5.2" xref="A1.26.26.26.m1.5.5.3.cmml"><mrow id="A1.26.26.26.m1.4.4.1.1" xref="A1.26.26.26.m1.4.4.1.1.cmml"><mrow id="A1.26.26.26.m1.4.4.1.1.2.2" xref="A1.26.26.26.m1.4.4.1.1.2.3.cmml"><msub id="A1.26.26.26.m1.4.4.1.1.1.1.1" xref="A1.26.26.26.m1.4.4.1.1.1.1.1.cmml"><mi id="A1.26.26.26.m1.4.4.1.1.1.1.1.2" xref="A1.26.26.26.m1.4.4.1.1.1.1.1.2.cmml">x</mi><mn id="A1.26.26.26.m1.4.4.1.1.1.1.1.3" xref="A1.26.26.26.m1.4.4.1.1.1.1.1.3.cmml">1</mn></msub><mo id="A1.26.26.26.m1.4.4.1.1.2.2.3" xref="A1.26.26.26.m1.4.4.1.1.2.3.cmml">,</mo><msub id="A1.26.26.26.m1.4.4.1.1.2.2.2" xref="A1.26.26.26.m1.4.4.1.1.2.2.2.cmml"><mi id="A1.26.26.26.m1.4.4.1.1.2.2.2.2" xref="A1.26.26.26.m1.4.4.1.1.2.2.2.2.cmml">x</mi><mn id="A1.26.26.26.m1.4.4.1.1.2.2.2.3" xref="A1.26.26.26.m1.4.4.1.1.2.2.2.3.cmml">2</mn></msub><mo id="A1.26.26.26.m1.4.4.1.1.2.2.4" xref="A1.26.26.26.m1.4.4.1.1.2.3.cmml">,</mo><mi id="A1.26.26.26.m1.1.1" xref="A1.26.26.26.m1.1.1.cmml">f</mi></mrow><mo id="A1.26.26.26.m1.4.4.1.1.3" stretchy="false" xref="A1.26.26.26.m1.4.4.1.1.3.cmml">←</mo><mi id="A1.26.26.26.m1.4.4.1.1.4" xref="A1.26.26.26.m1.4.4.1.1.4.cmml">i</mi></mrow><mo id="A1.26.26.26.m1.5.5.2.3" xref="A1.26.26.26.m1.5.5.3a.cmml">,</mo><mrow id="A1.26.26.26.m1.5.5.2.2.2" xref="A1.26.26.26.m1.5.5.2.2.1.cmml"><mi id="A1.26.26.26.m1.2.2" xref="A1.26.26.26.m1.2.2.cmml">j</mi><mo id="A1.26.26.26.m1.5.5.2.2.2.1" xref="A1.26.26.26.m1.5.5.2.2.1.cmml">,</mo><mtext id="A1.26.26.26.m1.3.3" xref="A1.26.26.26.m1.3.3a.cmml">False</mtext></mrow></mrow><annotation-xml encoding="MathML-Content" id="A1.26.26.26.m1.5b"><apply id="A1.26.26.26.m1.5.5.3.cmml" xref="A1.26.26.26.m1.5.5.2"><csymbol cd="ambiguous" id="A1.26.26.26.m1.5.5.3a.cmml" xref="A1.26.26.26.m1.5.5.2.3">formulae-sequence</csymbol><apply id="A1.26.26.26.m1.4.4.1.1.cmml" xref="A1.26.26.26.m1.4.4.1.1"><ci id="A1.26.26.26.m1.4.4.1.1.3.cmml" xref="A1.26.26.26.m1.4.4.1.1.3">←</ci><list id="A1.26.26.26.m1.4.4.1.1.2.3.cmml" xref="A1.26.26.26.m1.4.4.1.1.2.2"><apply id="A1.26.26.26.m1.4.4.1.1.1.1.1.cmml" xref="A1.26.26.26.m1.4.4.1.1.1.1.1"><csymbol cd="ambiguous" id="A1.26.26.26.m1.4.4.1.1.1.1.1.1.cmml" xref="A1.26.26.26.m1.4.4.1.1.1.1.1">subscript</csymbol><ci id="A1.26.26.26.m1.4.4.1.1.1.1.1.2.cmml" xref="A1.26.26.26.m1.4.4.1.1.1.1.1.2">𝑥</ci><cn id="A1.26.26.26.m1.4.4.1.1.1.1.1.3.cmml" type="integer" xref="A1.26.26.26.m1.4.4.1.1.1.1.1.3">1</cn></apply><apply id="A1.26.26.26.m1.4.4.1.1.2.2.2.cmml" xref="A1.26.26.26.m1.4.4.1.1.2.2.2"><csymbol cd="ambiguous" id="A1.26.26.26.m1.4.4.1.1.2.2.2.1.cmml" xref="A1.26.26.26.m1.4.4.1.1.2.2.2">subscript</csymbol><ci id="A1.26.26.26.m1.4.4.1.1.2.2.2.2.cmml" xref="A1.26.26.26.m1.4.4.1.1.2.2.2.2">𝑥</ci><cn id="A1.26.26.26.m1.4.4.1.1.2.2.2.3.cmml" type="integer" xref="A1.26.26.26.m1.4.4.1.1.2.2.2.3">2</cn></apply><ci id="A1.26.26.26.m1.1.1.cmml" xref="A1.26.26.26.m1.1.1">𝑓</ci></list><ci id="A1.26.26.26.m1.4.4.1.1.4.cmml" xref="A1.26.26.26.m1.4.4.1.1.4">𝑖</ci></apply><list id="A1.26.26.26.m1.5.5.2.2.1.cmml" xref="A1.26.26.26.m1.5.5.2.2.2"><ci id="A1.26.26.26.m1.2.2.cmml" xref="A1.26.26.26.m1.2.2">𝑗</ci><ci id="A1.26.26.26.m1.3.3a.cmml" xref="A1.26.26.26.m1.3.3"><mtext id="A1.26.26.26.m1.3.3.cmml" xref="A1.26.26.26.m1.3.3">False</mtext></ci></list></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.26.26.26.m1.5c">x_{1},x_{2},f\leftarrow i,j,\textup{False}</annotation><annotation encoding="application/x-llamapun" id="A1.26.26.26.m1.5d">italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , italic_f ← italic_i , italic_j , False</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.27.27.27"> return <math alttext="x_{1},x_{2},\delta,f" class="ltx_Math" display="inline" id="A1.27.27.27.m1.4"><semantics id="A1.27.27.27.m1.4a"><mrow id="A1.27.27.27.m1.4.4.2" xref="A1.27.27.27.m1.4.4.3.cmml"><msub id="A1.27.27.27.m1.3.3.1.1" xref="A1.27.27.27.m1.3.3.1.1.cmml"><mi id="A1.27.27.27.m1.3.3.1.1.2" xref="A1.27.27.27.m1.3.3.1.1.2.cmml">x</mi><mn id="A1.27.27.27.m1.3.3.1.1.3" xref="A1.27.27.27.m1.3.3.1.1.3.cmml">1</mn></msub><mo id="A1.27.27.27.m1.4.4.2.3" xref="A1.27.27.27.m1.4.4.3.cmml">,</mo><msub id="A1.27.27.27.m1.4.4.2.2" xref="A1.27.27.27.m1.4.4.2.2.cmml"><mi id="A1.27.27.27.m1.4.4.2.2.2" xref="A1.27.27.27.m1.4.4.2.2.2.cmml">x</mi><mn id="A1.27.27.27.m1.4.4.2.2.3" xref="A1.27.27.27.m1.4.4.2.2.3.cmml">2</mn></msub><mo id="A1.27.27.27.m1.4.4.2.4" xref="A1.27.27.27.m1.4.4.3.cmml">,</mo><mi id="A1.27.27.27.m1.1.1" xref="A1.27.27.27.m1.1.1.cmml">δ</mi><mo id="A1.27.27.27.m1.4.4.2.5" xref="A1.27.27.27.m1.4.4.3.cmml">,</mo><mi id="A1.27.27.27.m1.2.2" xref="A1.27.27.27.m1.2.2.cmml">f</mi></mrow><annotation-xml encoding="MathML-Content" id="A1.27.27.27.m1.4b"><list id="A1.27.27.27.m1.4.4.3.cmml" xref="A1.27.27.27.m1.4.4.2"><apply id="A1.27.27.27.m1.3.3.1.1.cmml" xref="A1.27.27.27.m1.3.3.1.1"><csymbol cd="ambiguous" id="A1.27.27.27.m1.3.3.1.1.1.cmml" xref="A1.27.27.27.m1.3.3.1.1">subscript</csymbol><ci id="A1.27.27.27.m1.3.3.1.1.2.cmml" xref="A1.27.27.27.m1.3.3.1.1.2">𝑥</ci><cn id="A1.27.27.27.m1.3.3.1.1.3.cmml" type="integer" xref="A1.27.27.27.m1.3.3.1.1.3">1</cn></apply><apply id="A1.27.27.27.m1.4.4.2.2.cmml" xref="A1.27.27.27.m1.4.4.2.2"><csymbol cd="ambiguous" id="A1.27.27.27.m1.4.4.2.2.1.cmml" xref="A1.27.27.27.m1.4.4.2.2">subscript</csymbol><ci id="A1.27.27.27.m1.4.4.2.2.2.cmml" xref="A1.27.27.27.m1.4.4.2.2.2">𝑥</ci><cn id="A1.27.27.27.m1.4.4.2.2.3.cmml" type="integer" xref="A1.27.27.27.m1.4.4.2.2.3">2</cn></apply><ci id="A1.27.27.27.m1.1.1.cmml" xref="A1.27.27.27.m1.1.1">𝛿</ci><ci id="A1.27.27.27.m1.2.2.cmml" xref="A1.27.27.27.m1.2.2">𝑓</ci></list></annotation-xml><annotation encoding="application/x-tex" id="A1.27.27.27.m1.4c">x_{1},x_{2},\delta,f</annotation><annotation encoding="application/x-llamapun" id="A1.27.27.27.m1.4d">italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , italic_δ , italic_f</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.29.29.34"> end for </div> <div class="ltx_listingline" id="A1.29.29.35"> </div> <div class="ltx_listingline" id="A1.28.28.28"> <math alttext="\nu\leftarrow\nu+1" class="ltx_Math" display="inline" id="A1.28.28.28.m1.1"><semantics id="A1.28.28.28.m1.1a"><mrow id="A1.28.28.28.m1.1.1" xref="A1.28.28.28.m1.1.1.cmml"><mi id="A1.28.28.28.m1.1.1.2" xref="A1.28.28.28.m1.1.1.2.cmml">ν</mi><mo id="A1.28.28.28.m1.1.1.1" stretchy="false" xref="A1.28.28.28.m1.1.1.1.cmml">←</mo><mrow id="A1.28.28.28.m1.1.1.3" xref="A1.28.28.28.m1.1.1.3.cmml"><mi id="A1.28.28.28.m1.1.1.3.2" xref="A1.28.28.28.m1.1.1.3.2.cmml">ν</mi><mo id="A1.28.28.28.m1.1.1.3.1" xref="A1.28.28.28.m1.1.1.3.1.cmml">+</mo><mn id="A1.28.28.28.m1.1.1.3.3" xref="A1.28.28.28.m1.1.1.3.3.cmml">1</mn></mrow></mrow><annotation-xml encoding="MathML-Content" id="A1.28.28.28.m1.1b"><apply id="A1.28.28.28.m1.1.1.cmml" xref="A1.28.28.28.m1.1.1"><ci id="A1.28.28.28.m1.1.1.1.cmml" xref="A1.28.28.28.m1.1.1.1">←</ci><ci id="A1.28.28.28.m1.1.1.2.cmml" xref="A1.28.28.28.m1.1.1.2">𝜈</ci><apply id="A1.28.28.28.m1.1.1.3.cmml" xref="A1.28.28.28.m1.1.1.3"><plus id="A1.28.28.28.m1.1.1.3.1.cmml" xref="A1.28.28.28.m1.1.1.3.1"></plus><ci id="A1.28.28.28.m1.1.1.3.2.cmml" xref="A1.28.28.28.m1.1.1.3.2">𝜈</ci><cn id="A1.28.28.28.m1.1.1.3.3.cmml" type="integer" xref="A1.28.28.28.m1.1.1.3.3">1</cn></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.28.28.28.m1.1c">\nu\leftarrow\nu+1</annotation><annotation encoding="application/x-llamapun" id="A1.28.28.28.m1.1d">italic_ν ← italic_ν + 1</annotation></semantics></math> </div> <div class="ltx_listingline" id="A1.29.29.36"> end for </div> <div class="ltx_listingline" id="A1.29.29.37"> </div> <div class="ltx_listingline" id="A1.29.29.38"> end for </div> <div class="ltx_listingline" id="A1.29.29.39"> </div> <div class="ltx_listingline" id="A1.29.29.29"> return <math alttext="x_{1},x_{2},\delta,f" class="ltx_Math" display="inline" id="A1.29.29.29.m1.4"><semantics id="A1.29.29.29.m1.4a"><mrow id="A1.29.29.29.m1.4.4.2" xref="A1.29.29.29.m1.4.4.3.cmml"><msub id="A1.29.29.29.m1.3.3.1.1" xref="A1.29.29.29.m1.3.3.1.1.cmml"><mi id="A1.29.29.29.m1.3.3.1.1.2" xref="A1.29.29.29.m1.3.3.1.1.2.cmml">x</mi><mn id="A1.29.29.29.m1.3.3.1.1.3" xref="A1.29.29.29.m1.3.3.1.1.3.cmml">1</mn></msub><mo id="A1.29.29.29.m1.4.4.2.3" xref="A1.29.29.29.m1.4.4.3.cmml">,</mo><msub id="A1.29.29.29.m1.4.4.2.2" xref="A1.29.29.29.m1.4.4.2.2.cmml"><mi id="A1.29.29.29.m1.4.4.2.2.2" xref="A1.29.29.29.m1.4.4.2.2.2.cmml">x</mi><mn id="A1.29.29.29.m1.4.4.2.2.3" xref="A1.29.29.29.m1.4.4.2.2.3.cmml">2</mn></msub><mo id="A1.29.29.29.m1.4.4.2.4" xref="A1.29.29.29.m1.4.4.3.cmml">,</mo><mi id="A1.29.29.29.m1.1.1" xref="A1.29.29.29.m1.1.1.cmml">δ</mi><mo id="A1.29.29.29.m1.4.4.2.5" xref="A1.29.29.29.m1.4.4.3.cmml">,</mo><mi id="A1.29.29.29.m1.2.2" xref="A1.29.29.29.m1.2.2.cmml">f</mi></mrow><annotation-xml encoding="MathML-Content" id="A1.29.29.29.m1.4b"><list id="A1.29.29.29.m1.4.4.3.cmml" xref="A1.29.29.29.m1.4.4.2"><apply id="A1.29.29.29.m1.3.3.1.1.cmml" xref="A1.29.29.29.m1.3.3.1.1"><csymbol cd="ambiguous" id="A1.29.29.29.m1.3.3.1.1.1.cmml" xref="A1.29.29.29.m1.3.3.1.1">subscript</csymbol><ci id="A1.29.29.29.m1.3.3.1.1.2.cmml" xref="A1.29.29.29.m1.3.3.1.1.2">𝑥</ci><cn id="A1.29.29.29.m1.3.3.1.1.3.cmml" type="integer" xref="A1.29.29.29.m1.3.3.1.1.3">1</cn></apply><apply id="A1.29.29.29.m1.4.4.2.2.cmml" xref="A1.29.29.29.m1.4.4.2.2"><csymbol cd="ambiguous" id="A1.29.29.29.m1.4.4.2.2.1.cmml" xref="A1.29.29.29.m1.4.4.2.2">subscript</csymbol><ci id="A1.29.29.29.m1.4.4.2.2.2.cmml" xref="A1.29.29.29.m1.4.4.2.2.2">𝑥</ci><cn id="A1.29.29.29.m1.4.4.2.2.3.cmml" type="integer" xref="A1.29.29.29.m1.4.4.2.2.3">2</cn></apply><ci id="A1.29.29.29.m1.1.1.cmml" xref="A1.29.29.29.m1.1.1">𝛿</ci><ci id="A1.29.29.29.m1.2.2.cmml" xref="A1.29.29.29.m1.2.2">𝑓</ci></list></annotation-xml><annotation encoding="application/x-tex" id="A1.29.29.29.m1.4c">x_{1},x_{2},\delta,f</annotation><annotation encoding="application/x-llamapun" id="A1.29.29.29.m1.4d">italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , italic_δ , italic_f</annotation></semantics></math> </div> </div> </figure> </section> <section class="ltx_appendix" id="A2"> <h2 class="ltx_title ltx_title_appendix"> Appendix B Segmentation masks with SExtractor </h2> <div class="ltx_para" id="A2.p1"> A popular image segmentation tool in astronomy is SExtractor121212<a class="ltx_ref ltx_url" href="https://sextractor.readthedocs.io/en/latest/index.html" title="">https://sextractor.readthedocs.io/en/latest/index.html</a> <cite class="ltx_cite ltx_citemacro_citep">(Bertin & Arnouts <a class="ltx_ref" href="https://arxiv.org/html/2404.18165v1#bib.bib8" title="">1996</a>)</cite>. This software is largely used for the detection of astronomical sources, background reduction, and photometry of astronomical images, being especially suitable for processing large field-of-view images. However, running SExtractor can be computationally expensive, especially compared to sigma clipping. We decided to compare the performance of both methods considering only those events that have a spectral classification available on the Transient Name Server (TNS)131313TNS is the International Astronomical Union’s official mechanism for reporting new astronomical transients since 2016, <a class="ltx_ref ltx_url ltx_font_typewriter" href="https://www.wis-tns.org/" title="">https://www.wis-tns.org/</a>.. We find that SExtractor retrieves 149 hostless candidates while sigma clipping retrieves 181 hostless candidates. By visually inspecting each candidate in the search for the presence of a potential host, we find that the SExtractor method has a <math alttext="\sim" class="ltx_Math" display="inline" id="A2.p1.1.m1.1"><semantics id="A2.p1.1.m1.1a"><mo id="A2.p1.1.m1.1.1" xref="A2.p1.1.m1.1.1.cmml">∼</mo><annotation-xml encoding="MathML-Content" id="A2.p1.1.m1.1b"><csymbol cd="latexml" id="A2.p1.1.m1.1.1.cmml" xref="A2.p1.1.m1.1.1">similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="A2.p1.1.m1.1c">\sim</annotation><annotation encoding="application/x-llamapun" id="A2.p1.1.m1.1d">∼</annotation></semantics></math> 15% contamination while the sigma clipping method has a <math alttext="\sim" class="ltx_Math" display="inline" id="A2.p1.2.m2.1"><semantics id="A2.p1.2.m2.1a"><mo id="A2.p1.2.m2.1.1" xref="A2.p1.2.m2.1.1.cmml">∼</mo><annotation-xml encoding="MathML-Content" id="A2.p1.2.m2.1b"><csymbol cd="latexml" id="A2.p1.2.m2.1.1.cmml" xref="A2.p1.2.m2.1.1">similar-to</csymbol></annotation-xml><annotation encoding="application/x-tex" id="A2.p1.2.m2.1c">\sim</annotation><annotation encoding="application/x-llamapun" id="A2.p1.2.m2.1d">∼</annotation></semantics></math> 22% contamination. Thus, considering that running SExtractor involves writing and reading files on the disk, which is not ideal when working with large volumes of data; and that the performance of both methods is similar, we favor the simpler sigma clipping as an image segmentation method. </div> <div class="ltx_pagination ltx_role_newpage"></div> </section> <section class="ltx_appendix" id="A3"> <h2 class="ltx_title ltx_title_appendix"> Appendix C Machine learning classified hostless candidates</h2> <div class="ltx_logical-block ltx_minipage ltx_align_middle" id="A3.1" style="width:252.9pt;"> <div class="ltx_para" id="A3.1.p1"> {ThreePartTable}{TableNotes} First column presents the IAU name of each object. The second column shows the corresponding ZTF internal name. The third and fourth column show right ascension and declination respectively. Column five shows the classification available on TNS. </div> <figure class="ltx_table" id="A3.T3"> <figcaption class="ltx_caption">Table 3: Fragment of the hostless candidate list without a reported classification on TNS. The full list can be found as supplementary material.</figcaption> <table class="ltx_tabular" id="A3.T3.5"> <tr class="ltx_tr" id="A3.T3.5.6"> <td class="ltx_td ltx_align_left ltx_border_tt" id="A3.T3.5.6.1">IAU Name</td> <td class="ltx_td ltx_align_left ltx_border_tt" id="A3.T3.5.6.2">ZTF Name</td> <td class="ltx_td ltx_align_center ltx_border_tt" id="A3.T3.5.6.3">R.A.</td> <td class="ltx_td ltx_align_center ltx_border_tt" id="A3.T3.5.6.4">Dec.</td> <td class="ltx_td ltx_align_left ltx_border_tt" id="A3.T3.5.6.5">Class</td> </tr> <tr class="ltx_tr" id="A3.T3.5.7"> <td class="ltx_td" id="A3.T3.5.7.1"></td> <td class="ltx_td" id="A3.T3.5.7.2"></td> <td class="ltx_td ltx_align_center" id="A3.T3.5.7.3">[J2000]</td> <td class="ltx_td ltx_align_center" id="A3.T3.5.7.4">[J2000]</td> <td class="ltx_td" id="A3.T3.5.7.5"></td> </tr> <tr class="ltx_tr" id="A3.T3.5.8"> <td class="ltx_td ltx_align_left ltx_border_t" id="A3.T3.5.8.1">AT 2016ayj</td> <td class="ltx_td ltx_align_left ltx_border_t" id="A3.T3.5.8.2"><a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF19adehksw" title="">ZTF19adehksw</a></td> <td class="ltx_td ltx_align_center ltx_border_t" id="A3.T3.5.8.3">03:06:45.60</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A3.T3.5.8.4">46:09:12.93</td> <td class="ltx_td ltx_align_left ltx_border_t" id="A3.T3.5.8.5">SN*_cand.</td> </tr> <tr class="ltx_tr" id="A3.T3.5.9"> <td class="ltx_td ltx_align_left" id="A3.T3.5.9.1">AT 2016ayl</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.9.2"><a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18acwwwsg" title="">ZTF18acwwwsg</a></td> <td class="ltx_td ltx_align_center" id="A3.T3.5.9.3">05:14:00.67</td> <td class="ltx_td ltx_align_center" id="A3.T3.5.9.4">55:21:57.81</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.9.5">SN*_cand.</td> </tr> <tr class="ltx_tr" id="A3.T3.5.10"> <td class="ltx_td ltx_align_left" id="A3.T3.5.10.1">AT 2016azn</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.10.2"><a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abxlizh" title="">ZTF22abxlizh</a></td> <td class="ltx_td ltx_align_center" id="A3.T3.5.10.3">10:06:54.81</td> <td class="ltx_td ltx_align_center" id="A3.T3.5.10.4">-14:25:37.80</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.10.5">AT cand.</td> </tr> <tr class="ltx_tr" id="A3.T3.5.11"> <td class="ltx_td ltx_align_left" id="A3.T3.5.11.1">AT 2017kn</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.11.2"><a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18aakpggd" title="">ZTF18aakpggd</a></td> <td class="ltx_td ltx_align_center" id="A3.T3.5.11.3">11:54:19.60</td> <td class="ltx_td ltx_align_center" id="A3.T3.5.11.4">57:57:50.77</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.11.5">QSO</td> </tr> <tr class="ltx_tr" id="A3.T3.5.12"> <td class="ltx_td ltx_align_left" id="A3.T3.5.12.1">AT 2018aod</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.12.2"><a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF23abofayp" title="">ZTF23abofayp</a></td> <td class="ltx_td ltx_align_center" id="A3.T3.5.12.3">03:25:09.82</td> <td class="ltx_td ltx_align_center" id="A3.T3.5.12.4">48:50:19.95</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.12.5">SN cand.</td> </tr> <tr class="ltx_tr" id="A3.T3.5.13"> <td class="ltx_td ltx_align_left" id="A3.T3.5.13.1">AT 2018cou</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.13.2"><a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18acxcpmo" title="">ZTF18acxcpmo</a></td> <td class="ltx_td ltx_align_center" id="A3.T3.5.13.3">14:15:23.73</td> <td class="ltx_td ltx_align_center" id="A3.T3.5.13.4">-20:00:54.17</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.13.5">SN</td> </tr> <tr class="ltx_tr" id="A3.T3.5.14"> <td class="ltx_td ltx_align_left" id="A3.T3.5.14.1">AT 2018ctv</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.14.2"><a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18abtgnsi" title="">ZTF18abtgnsi</a></td> <td class="ltx_td ltx_align_center" id="A3.T3.5.14.3">01:25:52.40</td> <td class="ltx_td ltx_align_center" id="A3.T3.5.14.4">-01:22:01.66</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.14.5">SN</td> </tr> <tr class="ltx_tr" id="A3.T3.5.15"> <td class="ltx_td ltx_align_left" id="A3.T3.5.15.1">AT 2018cyo</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.15.2"><a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF19aavprpy" title="">ZTF19aavprpy</a></td> <td class="ltx_td ltx_align_center" id="A3.T3.5.15.3">22:11:56.27</td> <td class="ltx_td ltx_align_center" id="A3.T3.5.15.4">-04:41:40.50</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.15.5">SN</td> </tr> <tr class="ltx_tr" id="A3.T3.5.16"> <td class="ltx_td ltx_align_left" id="A3.T3.5.16.1">AT 2018fou</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.16.2"><a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF18abtefbi" title="">ZTF18abtefbi</a></td> <td class="ltx_td ltx_align_center" id="A3.T3.5.16.3">23:05:32.51</td> <td class="ltx_td ltx_align_center" id="A3.T3.5.16.4">00:49:02.50</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.16.5">SN</td> </tr> <tr class="ltx_tr" id="A3.T3.5.17"> <td class="ltx_td ltx_align_left" id="A3.T3.5.17.1">AT 2018his</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.17.2"><a class="ltx_ref ltx_href" href="https://fink-portal.org/ZTF22abiflxl" title="">ZTF22abiflxl</a></td> <td class="ltx_td ltx_align_center" id="A3.T3.5.17.3">17:49:31.59</td> <td class="ltx_td ltx_align_center" id="A3.T3.5.17.4">17:15:37.23</td> <td class="ltx_td ltx_align_left" id="A3.T3.5.17.5">SN cand.</td> </tr> <tr class="ltx_tr" id="A3.T3.5.5"> <td class="ltx_td ltx_align_left ltx_border_b" id="A3.T3.1.1.1"><math alttext="\cdots" class="ltx_Math" display="inline" id="A3.T3.1.1.1.m1.1"><semantics id="A3.T3.1.1.1.m1.1a"><mi id="A3.T3.1.1.1.m1.1.1" mathvariant="normal" xref="A3.T3.1.1.1.m1.1.1.cmml">⋯</mi><annotation-xml encoding="MathML-Content" id="A3.T3.1.1.1.m1.1b"><ci id="A3.T3.1.1.1.m1.1.1.cmml" xref="A3.T3.1.1.1.m1.1.1">⋯</ci></annotation-xml><annotation encoding="application/x-tex" id="A3.T3.1.1.1.m1.1c">\cdots</annotation><annotation encoding="application/x-llamapun" id="A3.T3.1.1.1.m1.1d">⋯</annotation></semantics></math></td> <td class="ltx_td ltx_align_left ltx_border_b" id="A3.T3.2.2.2"><math alttext="\cdots" class="ltx_Math" display="inline" id="A3.T3.2.2.2.m1.1"><semantics id="A3.T3.2.2.2.m1.1a"><mi id="A3.T3.2.2.2.m1.1.1" mathvariant="normal" xref="A3.T3.2.2.2.m1.1.1.cmml">⋯</mi><annotation-xml encoding="MathML-Content" id="A3.T3.2.2.2.m1.1b"><ci id="A3.T3.2.2.2.m1.1.1.cmml" xref="A3.T3.2.2.2.m1.1.1">⋯</ci></annotation-xml><annotation encoding="application/x-tex" id="A3.T3.2.2.2.m1.1c">\cdots</annotation><annotation encoding="application/x-llamapun" id="A3.T3.2.2.2.m1.1d">⋯</annotation></semantics></math></td> <td class="ltx_td ltx_align_center ltx_border_b" id="A3.T3.3.3.3"><math alttext="\cdots" class="ltx_Math" display="inline" id="A3.T3.3.3.3.m1.1"><semantics id="A3.T3.3.3.3.m1.1a"><mi id="A3.T3.3.3.3.m1.1.1" mathvariant="normal" xref="A3.T3.3.3.3.m1.1.1.cmml">⋯</mi><annotation-xml encoding="MathML-Content" id="A3.T3.3.3.3.m1.1b"><ci id="A3.T3.3.3.3.m1.1.1.cmml" xref="A3.T3.3.3.3.m1.1.1">⋯</ci></annotation-xml><annotation encoding="application/x-tex" id="A3.T3.3.3.3.m1.1c">\cdots</annotation><annotation encoding="application/x-llamapun" id="A3.T3.3.3.3.m1.1d">⋯</annotation></semantics></math></td> <td class="ltx_td ltx_align_center ltx_border_b" id="A3.T3.4.4.4"><math alttext="\cdots" class="ltx_Math" display="inline" id="A3.T3.4.4.4.m1.1"><semantics id="A3.T3.4.4.4.m1.1a"><mi id="A3.T3.4.4.4.m1.1.1" mathvariant="normal" xref="A3.T3.4.4.4.m1.1.1.cmml">⋯</mi><annotation-xml encoding="MathML-Content" id="A3.T3.4.4.4.m1.1b"><ci id="A3.T3.4.4.4.m1.1.1.cmml" xref="A3.T3.4.4.4.m1.1.1">⋯</ci></annotation-xml><annotation encoding="application/x-tex" id="A3.T3.4.4.4.m1.1c">\cdots</annotation><annotation encoding="application/x-llamapun" id="A3.T3.4.4.4.m1.1d">⋯</annotation></semantics></math></td> <td class="ltx_td ltx_align_left ltx_border_b" id="A3.T3.5.5.5"><math alttext="\cdots" class="ltx_Math" display="inline" id="A3.T3.5.5.5.m1.1"><semantics id="A3.T3.5.5.5.m1.1a"><mi id="A3.T3.5.5.5.m1.1.1" mathvariant="normal" xref="A3.T3.5.5.5.m1.1.1.cmml">⋯</mi><annotation-xml encoding="MathML-Content" id="A3.T3.5.5.5.m1.1b"><ci id="A3.T3.5.5.5.m1.1.1.cmml" xref="A3.T3.5.5.5.m1.1.1">⋯</ci></annotation-xml><annotation encoding="application/x-tex" id="A3.T3.5.5.5.m1.1c">\cdots</annotation><annotation encoding="application/x-llamapun" id="A3.T3.5.5.5.m1.1d">⋯</annotation></semantics></math></td> </tr> </table> </figure> </div> </section> </article> </div> <footer class="ltx_page_footer"> <div class="ltx_page_logo">Generated on Sun Apr 28 12:27:34 2024 by <a class="ltx_LaTeXML_logo" href="http://dlmf.nist.gov/LaTeXML/">LaTeXML<img alt="Mascot Sammy" src="data:image/png;base64,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"/></a> </div></footer> </div> </body> </html>