{"id":"https://openalex.org/W7212324906","doi":"https://doi.org/10.48550/arxiv.2609.10689","title":"Wave optical imaging of an oscillating electric dipole orbiting a black hole","display_name":"Wave optical imaging of an oscillating electric dipole orbiting a black hole","publication_year":2026,"publication_date":"2026-09-09","ids":{"openalex":"https://openalex.org/W7212324906","doi":"https://doi.org/10.48550/arxiv.2609.10689"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.10689","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10689","pdf_url":"https://arxiv.org/pdf/2609.10689","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/2609.10689","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137346072","display_name":"Filipe Nazar\u00e9","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]},{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}],"countries":["DK","PT"],"is_corresponding":false,"raw_author_name":"Nazar\u00e9, Filipe","raw_affiliation_strings":["CENTRA , Departamento de F\u00edsica , Instituto Superior T\u00e9cnico -IST ,","Center of Gravity , Niels Bohr Institute , Blegdamsvej 17 , 2100 Copenhagen , Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CENTRA , Departamento de F\u00edsica , Instituto Superior T\u00e9cnico -IST ,","institution_ids":["https://openalex.org/I4387152517"]},{"raw_affiliation_string":"Center of Gravity , Niels Bohr Institute , Blegdamsvej 17 , 2100 Copenhagen , Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001106705","display_name":"Jo\u00e3o S. Santos","orcid":"https://orcid.org/0000-0003-1921-8758","observed_orcids":["https://orcid.org/0000-0003-1921-8758"]},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]},{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}],"countries":["DK","PT"],"is_corresponding":false,"raw_author_name":"Santos, Jo\u00e3o S.","raw_affiliation_strings":["CENTRA , Departamento de F\u00edsica , Instituto Superior T\u00e9cnico -IST ,","Center of Gravity , Niels Bohr Institute , Blegdamsvej 17 , 2100 Copenhagen , Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CENTRA , Departamento de F\u00edsica , Instituto Superior T\u00e9cnico -IST ,","institution_ids":["https://openalex.org/I4387152517"]},{"raw_affiliation_string":"Center of Gravity , Niels Bohr Institute , Blegdamsvej 17 , 2100 Copenhagen , Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123613638","display_name":"Vitor Cardoso","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cardoso, Vitor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014493800","display_name":"Jos\u00e9 Nat\u00e1rio","orcid":"https://orcid.org/0000-0003-0885-9867","observed_orcids":["https://orcid.org/0000-0003-0885-9867"]},"institutions":[{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Nat\u00e1rio, Jos\u00e9","raw_affiliation_strings":["CAMGSD , Departamento de Matem\u00e1tica , Instituto Superior T\u00e9cnico -IST ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CAMGSD , Departamento de Matem\u00e1tica , Instituto Superior T\u00e9cnico -IST ,","institution_ids":["https://openalex.org/I4387152517"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T10744","display_name":"Astrophysical Phenomena and Observations","score":0.6410999894142151,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10744","display_name":"Astrophysical Phenomena and Observations","score":0.6410999894142151,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.16419999301433563,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.14309999346733093,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rotating-black-holes","display_name":"rotating black holes","score":0.9940000176429749},{"id":"https://openalex.org/keywords/black-hole-perturbation-theory","display_name":"black hole perturbation theory","score":0.8619999885559082},{"id":"https://openalex.org/keywords/relativistic-beaming","display_name":"relativistic beaming","score":0.828000009059906},{"id":"https://openalex.org/keywords/gravitational-lensing","display_name":"gravitational lensing","score":0.9980000257492065},{"id":"https://openalex.org/keywords/einstein-ring","display_name":"Einstein ring","score":0.9919999837875366},{"id":"https://openalex.org/keywords/polarization-dependent-scattering","display_name":"polarization-dependent scattering","score":0.9739999771118164},{"id":"https://openalex.org/keywords/electromagnetic-radiation","display_name":"electromagnetic radiation","score":0.4480000138282776}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.9063000082969666},{"id":"https://openalex.org/C149773537","wikidata":"https://www.wikidata.org/wiki/Q12969754","display_name":"Electromagnetic radiation","level":2,"score":0.5846999883651733},{"id":"https://openalex.org/C173523689","wikidata":"https://www.wikidata.org/wiki/Q215589","display_name":"Dipole","level":2,"score":0.5388000011444092},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.5141000151634216},{"id":"https://openalex.org/C50341732","wikidata":"https://www.wikidata.org/wiki/Q880302","display_name":"Black hole (networking)","level":5,"score":0.5123999714851379},{"id":"https://openalex.org/C169852918","wikidata":"https://www.wikidata.org/wiki/Q390314","display_name":"Magnetic dipole","level":3,"score":0.45019999146461487},{"id":"https://openalex.org/C40745267","wikidata":"https://www.wikidata.org/wiki/Q497396","display_name":"Hawking radiation","level":3,"score":0.4481000006198883},{"id":"https://openalex.org/C60799052","wikidata":"https://www.wikidata.org/wiki/Q46221","display_name":"Electric field","level":2,"score":0.43720000982284546},{"id":"https://openalex.org/C28843909","wikidata":"https://www.wikidata.org/wiki/Q177625","display_name":"Electromagnetic field","level":2,"score":0.4318999946117401},{"id":"https://openalex.org/C82422596","wikidata":"https://www.wikidata.org/wiki/Q1094364","display_name":"Rotating black hole","level":3,"score":0.42640000581741333},{"id":"https://openalex.org/C190330329","wikidata":"https://www.wikidata.org/wiki/Q190035","display_name":"Gravitational wave","level":2,"score":0.4104999899864197},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.4027000069618225},{"id":"https://openalex.org/C153385146","wikidata":"https://www.wikidata.org/wiki/Q18335","display_name":"Radiation","level":2,"score":0.3959999978542328},{"id":"https://openalex.org/C202449340","wikidata":"https://www.wikidata.org/wiki/Q735135","display_name":"Electric dipole moment","level":3,"score":0.36239999532699585},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.3603000044822693},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.32739999890327454},{"id":"https://openalex.org/C115304011","wikidata":"https://www.wikidata.org/wiki/Q72755","display_name":"Schwarzschild radius","level":3,"score":0.3197000026702881},{"id":"https://openalex.org/C143715953","wikidata":"https://www.wikidata.org/wiki/Q332107","display_name":"Transition radiation","level":3,"score":0.3165000081062317},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.30399999022483826},{"id":"https://openalex.org/C30475298","wikidata":"https://www.wikidata.org/wiki/Q909554","display_name":"Computational physics","level":1,"score":0.30309998989105225},{"id":"https://openalex.org/C154815118","wikidata":"https://www.wikidata.org/wiki/Q453762","display_name":"Spinning","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C183915046","wikidata":"https://www.wikidata.org/wiki/Q1316152","display_name":"Charged black hole","level":4,"score":0.2851000130176544},{"id":"https://openalex.org/C149298590","wikidata":"https://www.wikidata.org/wiki/Q219708","display_name":"Magnetic monopole","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C203187862","wikidata":"https://www.wikidata.org/wiki/Q5357578","display_name":"Electric dipole transition","level":4,"score":0.2833000123500824},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C91748784","wikidata":"https://www.wikidata.org/wiki/Q11406","display_name":"Electromagnetism","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C174256460","wikidata":"https://www.wikidata.org/wiki/Q911364","display_name":"Perturbation theory (quantum mechanics)","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C188655511","wikidata":"https://www.wikidata.org/wiki/Q609501","display_name":"Micro black hole","level":4,"score":0.2671000063419342},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C14589660","wikidata":"https://www.wikidata.org/wiki/Q64122","display_name":"Electromagnetic pulse","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.10689","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10689","pdf_url":"https://arxiv.org/pdf/2609.10689","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":"doi:10.48550/arxiv.2609.10689","doi":"https://doi.org/10.48550/arxiv.2609.10689","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.10689","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:2609.10689","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10689","pdf_url":"https://arxiv.org/pdf/2609.10689","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/G1312727506","display_name":"Centro de An\u00e1lise Matem\u00e1tica, Geometria e Sistemas Din\u00e2micos","funder_award_id":"UID/PRR/04459/2025","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G1789019856","display_name":null,"funder_award_id":"VIL37766","funder_id":"https://openalex.org/F4320320943","funder_display_name":"Danmarks Grundforskningsfond"},{"id":"https://openalex.org/G2536870102","display_name":null,"funder_award_id":"Gravitas\u2013101052587","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G296744003","display_name":null,"funder_award_id":"DNRF184","funder_id":"https://openalex.org/F4320320943","funder_display_name":"Danmarks Grundforskningsfond"},{"id":"https://openalex.org/G3169205443","display_name":"Centro de An\u00e1lise Matem\u00e1tica, Geometria e Sistemas Din\u00e2micos","funder_award_id":"UID/04459/2025","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3492272913","display_name":null,"funder_award_id":"101052587","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4533005575","display_name":null,"funder_award_id":"VIL37766","funder_id":"https://openalex.org/F4320310490","funder_display_name":"Villum Fonden"},{"id":"https://openalex.org/G4669645064","display_name":"Gravitational Universe: Challenges and Opportunities","funder_award_id":"101007855","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4984070208","display_name":null,"funder_award_id":"101052587","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G5053941128","display_name":null,"funder_award_id":"101131233","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G5487836664","display_name":null,"funder_award_id":"101131233","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5759873967","display_name":null,"funder_award_id":"Gravitas-101052587","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G6645931917","display_name":null,"funder_award_id":"101007855","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320310490","display_name":"Villum Fonden","ror":"https://ror.org/007ww2d15"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320320847","display_name":"Science Foundation Ireland","ror":"https://ror.org/0271asj38"},{"id":"https://openalex.org/F4320320943","display_name":"Danmarks Grundforskningsfond","ror":"https://ror.org/00znyv691"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212324906.pdf","grobid_xml":"https://content.openalex.org/works/W7212324906.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W1965585193","https://openalex.org/W1994699824","https://openalex.org/W2017030612","https://openalex.org/W2070353143","https://openalex.org/W2110284565","https://openalex.org/W2123710893","https://openalex.org/W2134900351","https://openalex.org/W2142347153","https://openalex.org/W2167353723","https://openalex.org/W2252795400","https://openalex.org/W2765081049","https://openalex.org/W2798811027","https://openalex.org/W2808081211","https://openalex.org/W2943257677","https://openalex.org/W2982490442","https://openalex.org/W3005703510","https://openalex.org/W3008006659","https://openalex.org/W3012482296","https://openalex.org/W3138454662","https://openalex.org/W3200624720","https://openalex.org/W4281561162","https://openalex.org/W4287992231","https://openalex.org/W4366990670","https://openalex.org/W4384108836","https://openalex.org/W4391954502","https://openalex.org/W4391995600","https://openalex.org/W4399854407","https://openalex.org/W4403425309","https://openalex.org/W4405066590","https://openalex.org/W4405943122","https://openalex.org/W4409001729","https://openalex.org/W4410288695","https://openalex.org/W4413836634","https://openalex.org/W4414039382","https://openalex.org/W4415166303","https://openalex.org/W4416287446","https://openalex.org/W7131080546","https://openalex.org/W7138882004","https://openalex.org/W7152923686","https://openalex.org/W7170081038","https://openalex.org/W7171560961"],"related_works":["https://openalex.org/W2027345038","https://openalex.org/W2134900351","https://openalex.org/W4410288695","https://openalex.org/W4233606573","https://openalex.org/W2062846323","https://openalex.org/W1965027364","https://openalex.org/W3155771116","https://openalex.org/W6922468096","https://openalex.org/W1982875192","https://openalex.org/W7147711197"],"abstract_inverted_index":{"We":[0,18,52,67,83],"study":[1,84],"the":[2,20,41,89,105,108],"electromagnetic":[3,62,127],"radiation":[4,43,109,128],"and":[5,33,80],"wave-optical":[6,56],"imaging":[7,57],"of":[8,70,107,126],"an":[9,71],"oscillating":[10,27],"electric":[11,28,73],"dipole":[12,29],"orbiting":[13,72],"a":[14,25,55,60,99,114,120],"Kerr":[15,130],"black":[16,35],"hole.":[17],"derive":[19],"effective":[21],"4-current":[22],"associated":[23],"with":[24,95,104],"pointlike":[26],"in":[30,64,129],"curved":[31,65],"spacetime,":[32],"use":[34],"hole":[36],"perturbation":[37],"theory":[38],"to":[39],"compute":[40],"resulting":[42],"field":[44],"at":[45],"future":[46],"null":[47],"infinity,":[48],"from":[49],"first":[50],"principles.":[51],"then":[53],"develop":[54],"framework":[58],"for":[59,113,123],"moving":[61],"source":[63],"spacetime.":[66,131],"obtain":[68],"images":[69,90],"dipole,":[74],"displaying":[75],"relativistic":[76],"beaming,":[77],"gravitational":[78],"lensing,":[79],"Einstein":[81],"rings.":[82],"polarization-dependent":[85],"scattering":[86],"by":[87,92],"comparing":[88],"produced":[91],"spinning":[93],"dipoles":[94],"opposite":[96],"helicities,":[97],"finding":[98],"displacement":[100],"that":[101],"roughly":[102],"decreases":[103],"inverse":[106],"frequency,":[110],"as":[111],"expected":[112],"beyond-geometric-optics":[115,124],"effect.":[116],"Our":[117],"results":[118],"provide":[119],"first-principles":[121],"benchmark":[122],"descriptions":[125]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-12T00:00:00"}