{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:LHZ4WWEGAAI56LBATX2PCATDFD","short_pith_number":"pith:LHZ4WWEG","schema_version":"1.0","canonical_sha256":"59f3cb58860011df2c209df4f1026328f85c79807d191da22da7f8ef5ce0670c","source":{"kind":"arxiv","id":"2508.21409","version":3},"attestation_state":"computed","paper":{"title":"Analysis of quantities determining the critical inverse temperature in the annealed Potts model with Pareto vertex weights","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"A.J.E.M. Janssen","submitted_at":"2025-08-29T08:32:04Z","abstract_excerpt":"We consider in this work the crucial quantity $t_c$ that determines the critical inverse temperature $\\beta_c$ in the $q$-state Potts model on sparse rank-1 random graphs where the vertices are equipped with a Pareto weight density $(\\tau-1)\\,w^{-\\tau}\\,{\\cal X}_{[1,\\infty)}(w)$. It is shown in \\cite{ref1} that this $t_c$ is the unique positive zero of a function ${\\cal K}$ that is obtained by an appropriate combination of the stationarity condition and the criticality condition for the case the external field $B$ equals 0 and that $q\\geq3$ and $\\tau\\geq4$, see \\cite{ref1}, Theorem~1.14 and Th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2508.21409","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-08-29T08:32:04Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"66d504d7ccce82a9b017b89342915dcd1830c349c8dcbce7b9478af11024d951","abstract_canon_sha256":"3e9a19f865da3a06ec901a047e5e76c4053dc8f61f997033d5fcd868015e8066"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-15T01:20:47.541036Z","signature_b64":"xnFzjw+2f1OOOTZBLcDeQfLN0LhAh2SUz4rD/+1v8FuJLtkD+mvVkueymVtXjekHtzTowQpBo3JREBVMRp7IAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59f3cb58860011df2c209df4f1026328f85c79807d191da22da7f8ef5ce0670c","last_reissued_at":"2026-07-15T01:20:47.540059Z","signature_status":"signed_v1","first_computed_at":"2026-07-15T01:20:47.540059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analysis of quantities determining the critical inverse temperature in the annealed Potts model with Pareto vertex weights","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"A.J.E.M. Janssen","submitted_at":"2025-08-29T08:32:04Z","abstract_excerpt":"We consider in this work the crucial quantity $t_c$ that determines the critical inverse temperature $\\beta_c$ in the $q$-state Potts model on sparse rank-1 random graphs where the vertices are equipped with a Pareto weight density $(\\tau-1)\\,w^{-\\tau}\\,{\\cal X}_{[1,\\infty)}(w)$. It is shown in \\cite{ref1} that this $t_c$ is the unique positive zero of a function ${\\cal K}$ that is obtained by an appropriate combination of the stationarity condition and the criticality condition for the case the external field $B$ equals 0 and that $q\\geq3$ and $\\tau\\geq4$, see \\cite{ref1}, Theorem~1.14 and Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.21409","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.21409/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2508.21409","created_at":"2026-07-15T01:20:47.540527+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.21409v3","created_at":"2026-07-15T01:20:47.540527+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.21409","created_at":"2026-07-15T01:20:47.540527+00:00"},{"alias_kind":"pith_short_12","alias_value":"LHZ4WWEGAAI5","created_at":"2026-07-15T01:20:47.540527+00:00"},{"alias_kind":"pith_short_16","alias_value":"LHZ4WWEGAAI56LBA","created_at":"2026-07-15T01:20:47.540527+00:00"},{"alias_kind":"pith_short_8","alias_value":"LHZ4WWEG","created_at":"2026-07-15T01:20:47.540527+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LHZ4WWEGAAI56LBATX2PCATDFD","json":"https://pith.science/pith/LHZ4WWEGAAI56LBATX2PCATDFD.json","graph_json":"https://pith.science/api/pith-number/LHZ4WWEGAAI56LBATX2PCATDFD/graph.json","events_json":"https://pith.science/api/pith-number/LHZ4WWEGAAI56LBATX2PCATDFD/events.json","paper":"https://pith.science/paper/LHZ4WWEG"},"agent_actions":{"view_html":"https://pith.science/pith/LHZ4WWEGAAI56LBATX2PCATDFD","download_json":"https://pith.science/pith/LHZ4WWEGAAI56LBATX2PCATDFD.json","view_paper":"https://pith.science/paper/LHZ4WWEG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.21409&json=true","fetch_graph":"https://pith.science/api/pith-number/LHZ4WWEGAAI56LBATX2PCATDFD/graph.json","fetch_events":"https://pith.science/api/pith-number/LHZ4WWEGAAI56LBATX2PCATDFD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LHZ4WWEGAAI56LBATX2PCATDFD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LHZ4WWEGAAI56LBATX2PCATDFD/action/storage_attestation","attest_author":"https://pith.science/pith/LHZ4WWEGAAI56LBATX2PCATDFD/action/author_attestation","sign_citation":"https://pith.science/pith/LHZ4WWEGAAI56LBATX2PCATDFD/action/citation_signature","submit_replication":"https://pith.science/pith/LHZ4WWEGAAI56LBATX2PCATDFD/action/replication_record"}},"created_at":"2026-07-15T01:20:47.540527+00:00","updated_at":"2026-07-15T01:20:47.540527+00:00"}