{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:15:05Z","timestamp":1785402905604,"version":"3.56.0"},"reference-count":24,"publisher":"American Physical Society (APS)","issue":"6","license":[{"start":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T00:00:00Z","timestamp":1766448000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/link.aps.org\/licenses\/aps-default-license"}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2025,12,4]]},"DOI":"10.1103\/7tjt-m8s6","type":"journal-article","created":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T18:30:38Z","timestamp":1764873038000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Deterministic interrelation between elastic moduli in critically elastic materials"],"prefix":"10.1103","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-8843-3536","authenticated-orcid":true,"given":"Hongryol","family":"Jeon","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/047426m28","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Illinois Urbana-Champaign"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4770-3881","authenticated-orcid":true,"given":"Mahdi","family":"Sadjadi","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03efmqc40","id-type":"ROR","asserted-by":"publisher"}],"name":"Arizona State University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2148-3289","authenticated-orcid":true,"given":"Varda F.","family":"Hagh","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/047426m28","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Illinois Urbana-Champaign"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,12,23]]},"reference":[{"key":"7tjt-m8s6Cc1R1","doi-asserted-by":"publisher","DOI":"10.2307\/2311997","type":"journal-article"},{"key":"7tjt-m8s6Cc2R1","doi-asserted-by":"publisher","DOI":"10.1007\/s10659-006-9074-0","type":"journal-article"},{"key":"7tjt-m8s6Cc3R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4296-3","type":"book","volume-title":"Introduction to Linear Elasticity","author":"P.\u00a0L. Gould","year":"1994"},{"key":"7tjt-m8s6Cc4R1","volume-title":"The Linearized Theory of Elasticity","author":"W.\u00a0S. Slaughter","year":"2012","type":"book"},{"key":"7tjt-m8s6Cc5R1","doi-asserted-by":"publisher","DOI":"10.1080\/14786446408643668","type":"journal-article"},{"key":"7tjt-m8s6Cc6R1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7683(78)90052-5","type":"journal-article"},{"key":"7tjt-m8s6Cc7R1","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/87\/34004","type":"journal-article"},{"key":"7tjt-m8s6Cc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.215501","type":"journal-article"},{"key":"7tjt-m8s6Cc9R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.83.184205","type":"journal-article"},{"key":"7tjt-m8s6Cc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.84.174119","type":"journal-article"},{"key":"7tjt-m8s6Cc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.135501","type":"journal-article"},{"key":"7tjt-m8s6Cc12R1","doi-asserted-by":"publisher","DOI":"10.1088\/0034-4885\/78\/7\/073901","type":"journal-article"},{"key":"7tjt-m8s6Cc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.97.063001","type":"journal-article"},{"key":"7tjt-m8s6Cc14R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1502939112","type":"journal-article"},{"key":"7tjt-m8s6Cc15R1","unstructured":"V.\u00a0F. Hagh, On the rigidity of disordered networks, Ph.D. thesis, Arizona State University, 2018.","type":"other"},{"key":"7tjt-m8s6Cc16R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2022.108306","type":"journal-article"},{"key":"7tjt-m8s6Cc17R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.225501","type":"journal-article"},{"key":"7tjt-m8s6Cc18R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.98.100101","type":"journal-article"},{"key":"7tjt-m8s6Cc19R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1717442115","type":"journal-article"},{"key":"7tjt-m8s6Cc20R1","doi-asserted-by":"publisher","DOI":"10.1039\/C8SM01768A","type":"journal-article"},{"key":"7tjt-m8s6Cc21R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00977785","type":"journal-article"},{"key":"7tjt-m8s6Cc22R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(97)00069-0","type":"journal-article"},{"key":"7tjt-m8s6Cc23R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.88.062130","type":"journal-article"},{"key":"7tjt-m8s6Cc24R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1612139114","type":"journal-article"}],"container-title":["Physical Review E"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/7tjt-m8s6","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/7tjt-m8s6\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T12:32:42Z","timestamp":1766493162000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/7tjt-m8s6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,23]]},"references-count":24,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2025,12]]}},"URL":"https:\/\/doi.org\/10.1103\/7tjt-m8s6","relation":{},"ISSN":["2470-0045","2470-0053"],"issn-type":[{"value":"2470-0045","type":"print"},{"value":"2470-0053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,23]]},"assertion":[{"value":"2025-09-20","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"\u00a92025 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":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"American Physical Society","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"065507"}}