{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T15:13:02Z","timestamp":1775056382002,"version":"3.50.1"},"reference-count":125,"publisher":"American Physical Society (APS)","issue":"8","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100021856","name":"Ministero dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["CUP: B53C25001080001"],"award-info":[{"award-number":["CUP: B53C25001080001"]}],"id":[{"id":"10.13039\/501100021856","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004007","name":"Instituto Nazionale di Fisica Nucleare","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004007","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. D"],"accepted":{"date-parts":[[2026,2,20]]},"abstract":"<jats:p>We present an analytical and numerical investigation of the quasinormal excitation factors of ultracompact horizonless objects. These systems possess long-lived quasinormal modes with extremely small imaginary parts, originating from the effective cavity between the photon sphere and the object\u2019s interior. We show that the excitation of such modes is strongly suppressed, scaling with the imaginary part of their frequency, and therefore they contribute to the waveform only at very late times. This hierarchy naturally explains the structure of echo signals; the prompt ringdown is dominated by standard light-ring modes, the early echoes arise from moderately damped cavity modes, and only the latest echoes are governed by long-lived modes. Building on this, we propose a practical ringdown waveform model that combines ordinary black-hole quasinormal modes with cavity modes, capturing the complexity of the ringdown of horizonless ultracompact objects. We further demonstrate that the combination of small excitation factors and weak damping enhances the robustness of long-lived modes against localized perturbations, in contrast to the spectral instabilities affecting standard black-hole quasinormal modes. Finally, we extend the analysis of greybody factors to exotic compact objects and wormholes, showing that they remain stable under small deformations of the effective potential and thus represent robust observables. Our results provide a unified framework for understanding excitation, stability, and echoes in ultracompact horizonless objects, with direct implications for their spectral properties and gravitational-wave signatures.<\/jats:p>","DOI":"10.1103\/v7pv-y3qy","type":"journal-article","created":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T16:42:30Z","timestamp":1771605750000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Excitation factors for horizonless compact objects: Long-lived modes, echoes, and greybody factors"],"prefix":"10.1103","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-3942-7900","authenticated-orcid":true,"given":"Romeo","family":"Felice Rosato","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02be6w209","id-type":"ROR","asserted-by":"publisher"}],"name":"Sapienza Universit\u00e0 di Roma"},{"id":[{"id":"https:\/\/ror.org\/005ta0471","id-type":"ROR","asserted-by":"publisher"}],"name":"INFN"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3773-8354","authenticated-orcid":true,"given":"Shauvik","family":"Biswas","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0036p5w23","id-type":"ROR","asserted-by":"publisher"}],"name":"Indian Institute of Technology"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3343-3227","authenticated-orcid":true,"given":"Sumanta","family":"Chakraborty","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/050p6gz73","id-type":"ROR","asserted-by":"publisher"}],"name":"Indian Association for the Cultivation of Science"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4443-1761","authenticated-orcid":true,"given":"Paolo","family":"Pani","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02be6w209","id-type":"ROR","asserted-by":"publisher"}],"name":"Sapienza Universit\u00e0 di Roma"},{"id":[{"id":"https:\/\/ror.org\/005ta0471","id-type":"ROR","asserted-by":"publisher"}],"name":"INFN"}]}],"member":"16","published-online":{"date-parts":[[2026,4,1]]},"reference":[{"key":"v7pv-y3qyCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.108.1063","type":"journal-article"},{"key":"v7pv-y3qyCc2R1","volume-title":"The Mathematical Theory of Black Holes","author":"S. Chandrasekhar","year":"1985","type":"book"},{"key":"v7pv-y3qyCc4R1","doi-asserted-by":"publisher","DOI":"10.1007\/s10714-025-03408-y","type":"journal-article"},{"key":"v7pv-y3qyCc5R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.116.061102","type":"journal-article"},{"key":"v7pv-y3qyCc6R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.125.101102","type":"journal-article"},{"key":"v7pv-y3qyCc7R1","doi-asserted-by":"publisher","DOI":"10.1103\/kw5g-d732","type":"journal-article"},{"key":"v7pv-y3qyCc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/6c61-fm1n","type":"journal-article"},{"key":"v7pv-y3qyCc9R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/21\/4\/003","type":"journal-article"},{"key":"v7pv-y3qyCc10R1","doi-asserted-by":"publisher","DOI":"10.1086\/158109","type":"journal-article"},{"key":"v7pv-y3qyCc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.73.064030","type":"journal-article"},{"key":"v7pv-y3qyCc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.85.124056","type":"journal-article"},{"key":"v7pv-y3qyCc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.112.084080","type":"journal-article"},{"key":"v7pv-y3qyCc14R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/32\/24\/243001","type":"journal-article"},{"key":"v7pv-y3qyCc15R1","doi-asserted-by":"publisher","DOI":"10.1007\/s10714-018-2372-6","type":"journal-article"},{"key":"v7pv-y3qyCc16R1","doi-asserted-by":"publisher","DOI":"10.1007\/s41114-019-0020-4","type":"journal-article"},{"key":"v7pv-y3qyCc18R1","doi-asserted-by":"publisher","DOI":"10.1088\/1475-7516\/2020\/03\/050","type":"journal-article"},{"key":"v7pv-y3qyCc20R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/28\/9\/094013","type":"journal-article"},{"key":"v7pv-y3qyCc21R1","doi-asserted-by":"publisher","DOI":"10.1088\/1475-7516\/2023\/07\/068","type":"journal-article"},{"key":"v7pv-y3qyCc23R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/aa51f4","type":"journal-article"},{"key":"v7pv-y3qyCc24R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.96.084004","type":"journal-article"},{"key":"v7pv-y3qyCc26R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.117.101102","type":"journal-article"},{"key":"v7pv-y3qyCc27R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.105.124063","type":"journal-article"},{"key":"v7pv-y3qyCc28R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.108.043019","type":"journal-article"},{"key":"v7pv-y3qyCc29R1","doi-asserted-by":"publisher","DOI":"10.1038\/227936a0","type":"journal-article"},{"key":"v7pv-y3qyCc30R1","doi-asserted-by":"publisher","DOI":"10.12942\/lrr-1999-2","type":"journal-article"},{"key":"v7pv-y3qyCc31R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/26\/16\/163001","type":"journal-article"},{"key":"v7pv-y3qyCc32R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.83.793","type":"journal-article"},{"key":"v7pv-y3qyCc33R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.123.111102","type":"journal-article"},{"key":"v7pv-y3qyCc35R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.102.064053","type":"journal-article"},{"key":"v7pv-y3qyCc37R1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-31520-6","type":"journal-article"},{"key":"v7pv-y3qyCc38R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.89.104059","type":"journal-article"},{"key":"v7pv-y3qyCc39R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.105.L061501","type":"journal-article"},{"key":"v7pv-y3qyCc40R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.129.241103","type":"journal-article"},{"key":"v7pv-y3qyCc41R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.107.084027","type":"journal-article"},{"key":"v7pv-y3qyCc42R1","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/610\/1\/012044","type":"journal-article"},{"key":"v7pv-y3qyCc43R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.111103","type":"journal-article"},{"key":"v7pv-y3qyCc44R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.106.084011","type":"journal-article"},{"key":"v7pv-y3qyCc45R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.064043","type":"journal-article"},{"key":"v7pv-y3qyCc46R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.024043","type":"journal-article"},{"key":"v7pv-y3qyCc47R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.116.171101","type":"journal-article"},{"key":"v7pv-y3qyCc47R2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.117.089902","type":"journal-article"},{"key":"v7pv-y3qyCc48R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.94.084031","type":"journal-article"},{"key":"v7pv-y3qyCc49R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41550-017-0225-y","type":"journal-article"},{"key":"v7pv-y3qyCc50R1","doi-asserted-by":"publisher","DOI":"10.3390\/universe6030043","type":"journal-article"},{"key":"v7pv-y3qyCc51R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.53.4397","type":"journal-article"},{"key":"v7pv-y3qyCc52R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.101.104009","type":"journal-article"},{"key":"v7pv-y3qyCc53R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.11.031003","type":"journal-article"},{"key":"v7pv-y3qyCc54R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.104.084091","type":"journal-article"},{"key":"v7pv-y3qyCc55R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/ac5054","type":"journal-article"},{"key":"v7pv-y3qyCc56R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.107.064012","type":"journal-article"},{"key":"v7pv-y3qyCc57R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/ac8ddc","type":"journal-article"},{"key":"v7pv-y3qyCc58R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.108.104002","type":"journal-article"},{"key":"v7pv-y3qyCc59R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.044023","type":"journal-article"},{"key":"v7pv-y3qyCc60R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP12(2023)187","type":"journal-article"},{"key":"v7pv-y3qyCc61R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP05(2024)202","type":"journal-article"},{"key":"v7pv-y3qyCc63R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.108.104027","type":"journal-article"},{"key":"v7pv-y3qyCc64R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.064068","type":"journal-article"},{"key":"v7pv-y3qyCc65R1","doi-asserted-by":"publisher","DOI":"10.1007\/s11433-024-2435-5","type":"journal-article"},{"key":"v7pv-y3qyCc66R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.024016","type":"journal-article"},{"key":"v7pv-y3qyCc67R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.133.211401","type":"journal-article"},{"key":"v7pv-y3qyCc68R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.111.084011","type":"journal-article"},{"key":"v7pv-y3qyCc69R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/13\/10\/001","type":"journal-article"},{"key":"v7pv-y3qyCc70R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(99)00048-4","type":"journal-article"},{"key":"v7pv-y3qyCc71R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.76.061503","type":"journal-article"},{"key":"v7pv-y3qyCc72R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.76.084007","type":"journal-article"},{"key":"v7pv-y3qyCc73R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.80.024021","type":"journal-article"},{"key":"v7pv-y3qyCc74R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.82.104028","type":"journal-article"},{"key":"v7pv-y3qyCc75R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.103.104018","type":"journal-article"},{"key":"v7pv-y3qyCc76R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.103.104017","type":"journal-article"},{"key":"v7pv-y3qyCc77R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.105.064046","type":"journal-article"},{"key":"v7pv-y3qyCc78R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.130.081401","type":"journal-article"},{"key":"v7pv-y3qyCc79R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.130.081402","type":"journal-article"},{"key":"v7pv-y3qyCc80R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.108.L021501","type":"journal-article"},{"key":"v7pv-y3qyCc81R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2023.116432","type":"journal-article"},{"key":"v7pv-y3qyCc82R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.044069","type":"journal-article"},{"key":"v7pv-y3qyCc82R2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.049902","type":"journal-article"},{"key":"v7pv-y3qyCc83R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.044048","type":"journal-article"},{"key":"v7pv-y3qyCc84R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.L101503","type":"journal-article"},{"key":"v7pv-y3qyCc85R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.124029","type":"journal-article"},{"key":"v7pv-y3qyCc86R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.124028","type":"journal-article"},{"key":"v7pv-y3qyCc87R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.104050","type":"journal-article"},{"key":"v7pv-y3qyCc88R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.9.041060","type":"journal-article"},{"key":"v7pv-y3qyCc89R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.101.044033","type":"journal-article"},{"key":"v7pv-y3qyCc90R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.108.104020","type":"journal-article"},{"key":"v7pv-y3qyCc91R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.5.2439","type":"journal-article"},{"key":"v7pv-y3qyCc92R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.49.883","type":"journal-article"},{"key":"v7pv-y3qyCc93R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.59.044017","type":"journal-article"},{"key":"v7pv-y3qyCc94R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.104005","type":"journal-article"},{"key":"v7pv-y3qyCc95R1","doi-asserted-by":"publisher","DOI":"10.1103\/2brx-xnyr","type":"journal-article"},{"key":"v7pv-y3qyCc96R1","doi-asserted-by":"publisher","DOI":"10.1103\/4yvq-57x6","type":"journal-article"},{"key":"v7pv-y3qyCc97R1","doi-asserted-by":"publisher","DOI":"10.1088\/1475-7516\/2023\/04\/013","type":"journal-article"},{"key":"v7pv-y3qyCc98R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.104028","type":"journal-article"},{"key":"v7pv-y3qyCc99R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.064086","type":"journal-article"},{"key":"v7pv-y3qyCc100R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02345020","type":"journal-article"},{"key":"v7pv-y3qyCc100R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01608497","type":"journal-article"},{"key":"v7pv-y3qyCc101R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.L121501","type":"journal-article"},{"key":"v7pv-y3qyCc102R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.084070","type":"journal-article"},{"key":"v7pv-y3qyCc104R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.96.084002","type":"journal-article"},{"key":"v7pv-y3qyCc105R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.96.104047","type":"journal-article"},{"key":"v7pv-y3qyCc106R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.96.082004","type":"journal-article"},{"key":"v7pv-y3qyCc107R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.133.031401","type":"journal-article"},{"key":"v7pv-y3qyCc108R1","doi-asserted-by":"publisher","DOI":"10.1002\/lpor.201700113","type":"journal-article"},{"key":"v7pv-y3qyCc109R1","unstructured":"L.\u2009A. Sheikh, Scattering resonances and pseudospectrum: stability and completeness aspects in optical and gravitational systems, Ph.D. thesis, Institut de Math\u00e9matiques de Bourgogne [Dijon], France, 2022.","type":"other"},{"key":"v7pv-y3qyCc110R1","volume-title":"Lorentzian Wormholes: From Einstein to Hawking","author":"M. Visser","year":"1995","type":"book"},{"key":"v7pv-y3qyCc111R1","doi-asserted-by":"publisher","DOI":"10.1088\/1475-7516\/2020\/04\/016","type":"journal-article"},{"key":"v7pv-y3qyCc112R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.34.384","type":"journal-article"},{"key":"v7pv-y3qyCc113R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.74.104020","type":"journal-article"},{"key":"v7pv-y3qyCc114R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.110.024042","type":"journal-article"},{"key":"v7pv-y3qyCc115R1","doi-asserted-by":"publisher","DOI":"10.1088\/1475-7516\/2020\/01\/052","type":"journal-article"},{"key":"v7pv-y3qyCc116R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.107.044012","type":"journal-article"},{"key":"v7pv-y3qyCc117R1","doi-asserted-by":"publisher","DOI":"10.1103\/82lx-g26j","type":"journal-article"},{"key":"v7pv-y3qyCc118R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.111.084051","type":"journal-article"},{"key":"v7pv-y3qyCc119R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.90.044069","type":"journal-article"},{"key":"v7pv-y3qyCc120R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.97.024040","type":"journal-article"},{"key":"v7pv-y3qyCc121R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.106.024041","type":"journal-article"},{"key":"v7pv-y3qyCc122R1","first-page":"1","type":"journal-article","volume":"65","author":"A.\u2009A. Starobinskil","year":"1974","journal-title":"Sov. Phys. JETP","ISSN":"https:\/\/id.crossref.org\/issn\/0038-5646","issn-type":"print"},{"key":"v7pv-y3qyCc123R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.99.064007","type":"journal-article"},{"key":"v7pv-y3qyCc124R1","first-page":"319","type":"journal-article","volume":"46","author":"M. Zworski","year":"1999","journal-title":"Not. Am. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9920","issn-type":"print"},{"key":"v7pv-y3qyCc125R1","doi-asserted-by":"publisher","DOI":"10.1088\/1475-7516\/2016\/12\/043","type":"journal-article"},{"key":"v7pv-y3qyCc127R1","doi-asserted-by":"publisher","DOI":"10.1103\/ht2n-vvvh","type":"journal-article"},{"key":"v7pv-y3qyCc128R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.96.064045","type":"journal-article"},{"key":"v7pv-y3qyCc129R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.211102","type":"journal-article"},{"key":"v7pv-y3qyCc132R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.131.111401","type":"journal-article"},{"key":"v7pv-y3qyCc133R1","doi-asserted-by":"publisher","DOI":"10.1142\/S0217751X13400186","type":"journal-article"},{"key":"v7pv-y3qyCc134R1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-19000-6","type":"journal-article"}],"container-title":["Physical Review D"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/v7pv-y3qy","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/v7pv-y3qy\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T13:31:04Z","timestamp":1775050264000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/v7pv-y3qy"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,1]]},"references-count":125,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2026,4]]}},"URL":"https:\/\/doi.org\/10.1103\/v7pv-y3qy","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2511.08692","asserted-by":"subject"}]},"ISSN":["2470-0010","2470-0029"],"issn-type":[{"value":"2470-0010","type":"print"},{"value":"2470-0029","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,1]]},"assertion":[{"value":"2025-11-21","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"084002"}}