{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,3]],"date-time":"2026-11-03T14:48:29Z","timestamp":1793717309682,"version":"4.6.1"},"reference-count":51,"publisher":"American Physical Society (APS)","issue":"11","license":[{"start":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:00:00Z","timestamp":1773792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/link.aps.org\/licenses\/aps-default-license"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00618\/2020"],"award-info":[{"award-number":["UIDB\/00618\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDP\/00618\/2020"],"award-info":[{"award-number":["UIDP\/00618\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/00618\/2025"],"award-info":[{"award-number":["UID\/00618\/2025"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["2021.05649.BD"],"award-info":[{"award-number":["2021.05649.BD"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2026,2,3]]},"DOI":"10.1103\/kwmh-6ccs","type":"journal-article","created":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T19:06:19Z","timestamp":1770145579000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Robust Critical Connectivity Threshold in Ranked Percolation of Granular Packings"],"prefix":"10.1103","volume":"136","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3726-3210","authenticated-orcid":true,"given":"Vasco C.","family":"Braz","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03nb7yk44","id-type":"ROR","asserted-by":"publisher"}],"name":"Centro de F\u00edsica Te\u00f3rica e Computacional"},{"id":[{"id":"https:\/\/ror.org\/01c27hj86","id-type":"ROR","asserted-by":"publisher"}],"name":"Faculdade de Ci\u00eancias da Universidade de Lisboa"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1677-6060","authenticated-orcid":true,"given":"N.\u2009A.\u2009M.","family":"Ara\u00fajo","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03nb7yk44","id-type":"ROR","asserted-by":"publisher"}],"name":"Centro de F\u00edsica Te\u00f3rica e Computacional"},{"id":[{"id":"https:\/\/ror.org\/01c27hj86","id-type":"ROR","asserted-by":"publisher"}],"name":"Faculdade de Ci\u00eancias da Universidade de Lisboa"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,3,18]]},"reference":[{"key":"kwmh-6ccsCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.68.1259","type":"journal-article"},{"key":"kwmh-6ccsCc2R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1383168","type":"journal-article"},{"key":"kwmh-6ccsCc3R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.89.025002","type":"journal-article"},{"key":"kwmh-6ccsCc4R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-6355-3","type":"book","volume-title":"Random Heterogeneous Materials: Microstructure and Macroscopic Properties","author":"S. Torquato","year":"2002"},{"key":"kwmh-6ccsCc5R1","doi-asserted-by":"publisher","DOI":"10.1039\/b802672f","type":"journal-article"},{"key":"kwmh-6ccsCc6R1","doi-asserted-by":"publisher","DOI":"10.1093\/comnet\/cny005","type":"journal-article"},{"key":"kwmh-6ccsCc7R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6633\/aadc3c","type":"journal-article"},{"key":"kwmh-6ccsCc8R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.269.5223.513","type":"journal-article"},{"key":"kwmh-6ccsCc9R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.57.3164","type":"journal-article"},{"key":"kwmh-6ccsCc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.85.011304","type":"journal-article"},{"key":"kwmh-6ccsCc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.90.015006","type":"journal-article"},{"key":"kwmh-6ccsCc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.94.032908","type":"journal-article"},{"key":"kwmh-6ccsCc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.198002","type":"journal-article"},{"key":"kwmh-6ccsCc14R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-31732-3","type":"journal-article"},{"key":"kwmh-6ccsCc15R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(97)00069-0","type":"journal-article"},{"key":"kwmh-6ccsCc16R1","doi-asserted-by":"publisher","DOI":"10.1051\/anphys:2006003","type":"journal-article"},{"key":"kwmh-6ccsCc17R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.87.244301","type":"journal-article"},{"key":"kwmh-6ccsCc18R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.133.238201","type":"journal-article"},{"key":"kwmh-6ccsCc19R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-45483-w","type":"journal-article"},{"key":"kwmh-6ccsCc20R1","doi-asserted-by":"publisher","DOI":"10.1115\/1.4068059","type":"journal-article"},{"key":"kwmh-6ccsCc21R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.134.038201","type":"journal-article"},{"key":"kwmh-6ccsCc22R1","doi-asserted-by":"publisher","DOI":"10.1039\/D4SM01324G","type":"journal-article"},{"key":"kwmh-6ccsCc23R1","doi-asserted-by":"publisher","DOI":"10.1038\/42831","type":"journal-article"},{"key":"kwmh-6ccsCc24R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.110.014901","type":"journal-article"},{"key":"kwmh-6ccsCc25R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ces.2005.02.015","type":"journal-article"},{"key":"kwmh-6ccsCc26R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.powtec.2010.04.014","type":"journal-article"},{"key":"kwmh-6ccsCc27R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.powtec.2017.02.024","type":"journal-article"},{"key":"kwmh-6ccsCc28R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cjche.2019.02.004","type":"journal-article"},{"key":"kwmh-6ccsCc29R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.028002","type":"journal-article"},{"key":"kwmh-6ccsCc30R1","doi-asserted-by":"publisher","DOI":"10.1063\/PT.3.5077","type":"journal-article"},{"key":"kwmh-6ccsCc31R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.powtec.2025.121088","type":"journal-article"},{"key":"kwmh-6ccsCc32R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.powtec.2022.117248","type":"journal-article"},{"key":"kwmh-6ccsCc33R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.powtec.2022.117799","type":"journal-article"},{"key":"kwmh-6ccsCc34R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-023-00676-y","type":"journal-article"},{"key":"kwmh-6ccsCc35R1","doi-asserted-by":"publisher","DOI":"10.1140\/epjst\/e2014-02266-y","type":"journal-article"},{"key":"kwmh-6ccsCc36R1","doi-asserted-by":"publisher","DOI":"10.1007\/s11440-007-0041-0","type":"journal-article"},{"key":"kwmh-6ccsCc37R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.96.022902","type":"journal-article"},{"key":"kwmh-6ccsCc38R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.83.041301","type":"journal-article"},{"key":"kwmh-6ccsCc39R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.85.011301","type":"journal-article"},{"key":"kwmh-6ccsCc40R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/kwmh-6ccs, for a description of the methods used to construct the contact networks, additional details on simulation parameters and outcomes, and the full derivation of the analytical results discussed in the text, which includes Refs.\u00a0[41\u201347].","type":"other"},{"key":"kwmh-6ccsCc41R1","volume-title":"Computational Granular Dynamics: Models and Algorithms","author":"T. P\u00f6schel","year":"2005","type":"book"},{"key":"kwmh-6ccsCc42R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.041127","type":"journal-article"},{"key":"kwmh-6ccsCc43R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.86.036106","type":"journal-article"},{"key":"kwmh-6ccsCc44R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.78.051105","type":"journal-article"},{"key":"kwmh-6ccsCc45R1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780199695119.001.0001","type":"book","volume-title":"The Nature of Complex Networks","author":"S.\u2009N. Dorogovtsev","year":"2022"},{"key":"kwmh-6ccsCc46R1","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780199206650.001.0001","type":"book","volume-title":"Networks: An Introduction","author":"M. Newman","year":"2010"},{"key":"kwmh-6ccsCc47R1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240060204","type":"journal-article"},{"key":"kwmh-6ccsCc48R1","unstructured":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT), Project UIDB\/00618\/2020,  (2020).","type":"other"},{"key":"kwmh-6ccsCc49R1","unstructured":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT), Project UIDP\/00618\/2020,  (2020).","type":"other"},{"key":"kwmh-6ccsCc50R1","unstructured":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT), Grant 2021.05649.BD,  (2021).","type":"other"},{"key":"kwmh-6ccsCc51R1","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.18494296","type":"dataset"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/kwmh-6ccs","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/kwmh-6ccs\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T19:31:06Z","timestamp":1774294266000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/kwmh-6ccs"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,18]]},"references-count":51,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2026,3]]}},"URL":"https:\/\/doi.org\/10.1103\/kwmh-6ccs","relation":{},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,18]]},"assertion":[{"value":"2025-05-08","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"\u00a9 2026 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":"American Physical Society","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"118202"}}