{"id":"https://openalex.org/W7220034879","doi":"https://doi.org/10.48550/arxiv.2610.10257","title":"First-order $\u0393$-expansion for entropic optimal transport with non-degenerate costs","display_name":"First-order $\u0393$-expansion for entropic optimal transport with non-degenerate costs","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220034879","doi":"https://doi.org/10.48550/arxiv.2610.10257"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10257","pdf_url":"https://arxiv.org/pdf/2610.10257","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.10257","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064926820","display_name":"Luca Nenna","orcid":"https://orcid.org/0000-0003-2540-1700","observed_orcids":["https://orcid.org/0000-0003-2540-1700"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I185839726","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266","country_code":"FR","type":"education","lineage":["https://openalex.org/I185839726"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nenna, Luca","raw_affiliation_strings":["Institut Universitaire de France , Paris , France","Universit\u00e9 Paris-Saclay , CNRS , Laboratoire de math\u00e9matiques d'Orsay , ParMA , Inria Saclay , 91405 , Orsay , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Universitaire de France , Paris , France","institution_ids":["https://openalex.org/I185839726"]},{"raw_affiliation_string":"Universit\u00e9 Paris-Saclay , CNRS , Laboratoire de math\u00e9matiques d'Orsay , ParMA , Inria Saclay , 91405 , Orsay , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023737340","display_name":"Brendan Pass","orcid":"https://orcid.org/0000-0003-0753-0381","observed_orcids":["https://orcid.org/0000-0003-0753-0381"]},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]},{"id":"https://openalex.org/I4405261691","display_name":"MOKAPLAN: Avanc\u00e9es en calcul num\u00e9rique des variations","ror":"https://ror.org/05pp95825","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4405257605","https://openalex.org/I4405261691"]}],"countries":["CA","FR"],"is_corresponding":false,"raw_author_name":"Pass, Brendan","raw_affiliation_strings":["Department of Mathematical and Statistical Sciences , 632 CAB , University of Alberta , Edmonton , Alberta , Canada , T6G 2G1","MOKAPLAN , Inria Paris , Paris , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Statistical Sciences , 632 CAB , University of Alberta , Edmonton , Alberta , Canada , T6G 2G1","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"MOKAPLAN , Inria Paris , Paris , France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4405261691"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041573575","display_name":"Paul Pegon","orcid":"https://orcid.org/0009-0005-2113-2816","observed_orcids":["https://orcid.org/0009-0005-2113-2816"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]},{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pegon, Paul","raw_affiliation_strings":["CEREMADE , CNRS UMR 7534 , Universit\u00e9 Paris-Dauphine -PSL , Paris , France &"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEREMADE , CNRS UMR 7534 , Universit\u00e9 Paris-Dauphine -PSL , Paris , France &","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I56435720"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5120025934","display_name":"Louis Tocquec","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Tocquec, Louis","raw_affiliation_strings":["Universit\u00e9 Paris-Saclay , CNRS , Laboratoire de math\u00e9matiques d'Orsay & MOKAPLAN , Inria Paris , 75016 Paris , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Saclay , CNRS , Laboratoire de math\u00e9matiques d'Orsay & MOKAPLAN , Inria Paris , 75016 Paris , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":10,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy-regularized-optimal-transport","display_name":"entropy-regularized optimal transport","score":0.9739999771118164},{"id":"https://openalex.org/keywords/first-order-asymptotics","display_name":"first-order asymptotics","score":0.6359999775886536},{"id":"https://openalex.org/keywords/gibbs-measures","display_name":"Gibbs measures","score":0.8080000281333923},{"id":"https://openalex.org/keywords/laplace-s-method","display_name":"Laplace method","score":0.7770000100135803},{"id":"https://openalex.org/keywords/duality-gap","display_name":"duality gap","score":0.8849999904632568},{"id":"https://openalex.org/keywords/contact-set","display_name":"contact set","score":0.7390000224113464},{"id":"https://openalex.org/keywords/sinkhorn-algorithm","display_name":"Sinkhorn algorithm","score":0.7689999938011169},{"id":"https://openalex.org/keywords/kullback-leibler-divergence","display_name":"Kullback-Leibler divergence","score":0.42100000381469727}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6712999939918518},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.588699996471405},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.520799994468689},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.48570001125335693},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4731999933719635},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.445499986410141},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43950000405311584},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4235000014305115},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41510000824928284},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.4090999960899353},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4016999900341034},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.3659999966621399},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C127233936","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Entropy maximization","level":3,"score":0.29510000348091125},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.2919999957084656},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.26829999685287476},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2610.10257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10257","pdf_url":"https://arxiv.org/pdf/2610.10257","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05774627v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05774627v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-05774627v2","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05774627v2","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2610.10257","doi":"https://doi.org/10.48550/arxiv.2610.10257","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10257","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.10257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10257","pdf_url":"https://arxiv.org/pdf/2610.10257","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6038677436","display_name":"Generalised Optimal Transport and Applications","funder_award_id":"ANR-23-CE46-0001","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6885101416","display_name":null,"funder_award_id":"04864-2024","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G7080048889","display_name":null,"funder_award_id":"ANR-23","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320324478","display_name":"Fondation Math\u00e9matique Jacques Hadamard","ror":"https://ror.org/0153me927"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220034879.pdf","grobid_xml":"https://content.openalex.org/works/W7220034879.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1612648786","https://openalex.org/W1990283121","https://openalex.org/W2045361520","https://openalex.org/W2081896234","https://openalex.org/W2096509975","https://openalex.org/W2142515208","https://openalex.org/W2337227421","https://openalex.org/W2952391864","https://openalex.org/W2962643425","https://openalex.org/W2988047989","https://openalex.org/W4255839052","https://openalex.org/W4299907955","https://openalex.org/W4391483226","https://openalex.org/W4414839321","https://openalex.org/W4417142170","https://openalex.org/W7155489953"],"related_works":["https://openalex.org/W7155489953","https://openalex.org/W7117147915","https://openalex.org/W4410478905","https://openalex.org/W4281755449","https://openalex.org/W2291607900","https://openalex.org/W7000196050","https://openalex.org/W4321854409","https://openalex.org/W4411911684","https://openalex.org/W7214660555","https://openalex.org/W3033956584"],"abstract_inverted_index":{"Entropy-regularized":[0],"optimal":[1,10],"transport":[2],"(EOT)":[3],"has":[4],"become":[5],"a":[6,43,49,60],"key":[7],"tool":[8],"in":[9],"transport,":[11],"providing":[12],"both":[13],"theoretical":[14],"insight":[15],"and":[16,75,93,106],"efficient":[17],"computation":[18],"via":[19],"the":[20,25,31,40,55,64,69,72,87,90,94,99,110],"Sinkhorn":[21],"algorithm.":[22],"We":[23],"study":[24],"first-order":[26],"\\(\u0393\\)-expansion":[27,78],"of":[28,42,63,71,109,119],"EOT":[29,38,111],"as":[30,39],"regularization":[32],"parameter":[33],"\\(\\varepsilon\\)":[34],"vanishes,":[35],"by":[36],"rewriting":[37],"minimization":[41],"relative":[44],"entropy":[45],"with":[46,54],"respect":[47],"to":[48,114],"Gibbs":[50,73],"measure":[51],"\\(\\gibbs\\)":[52],"associated":[53],"duality":[56,88],"gap":[57],"energy.":[58],"Using":[59],"mild":[61],"extension":[62],"Laplace":[65],"method,":[66],"we":[67],"prove":[68],"convergence":[70],"measures":[74],"derive":[76],"this":[77,117],"for":[79,116],"non-degenerate":[80],"ground":[81,120],"costs,":[82,121],"under":[83],"suitable":[84],"assumptions":[85],"on":[86],"gap,":[89],"contact":[91],"set":[92],"marginals.":[95],"This":[96],"yields":[97],"at":[98],"same":[100],"time":[101],"an":[102,107],"entropic":[103],"selection":[104],"principle":[105],"expansion":[108],"cost":[112],"up":[113],"\\(o(\\varepsilon)\\)":[115],"class":[118],"generalizing":[122],"existing":[123],"results.":[124]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-05T00:00:00"}
