{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PCVLMIG334PNIZRGZ5GJYWJEJY","short_pith_number":"pith:PCVLMIG3","schema_version":"1.0","canonical_sha256":"78aab620dbdf1ed46626cf4c9c59244e1a85cef3eb59575a3ffb2471447921c6","source":{"kind":"arxiv","id":"1412.2522","version":1},"attestation_state":"computed","paper":{"title":"The Potts and random-cluster models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Geoffrey R. Grimmett","submitted_at":"2014-12-08T11:36:13Z","abstract_excerpt":"This is a short account of connections between the Tutte polynomial and the Ising, Potts, and random-cluster models. The four principal elements are the Ising model of 1925, the Tutte polynomial of 1947, the Potts model of 1952, and the random-cluster model of 1972."},"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":"1412.2522","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-08T11:36:13Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"c71467442ea124afa5181eaa2d10e4b6a9a814a4af81f6f2ba764cd3114e7789","abstract_canon_sha256":"0b367ad69743bcb83e55406f523dc6db82306c2da22bbfe2eb12c4072058dac5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:57.670149Z","signature_b64":"lsh5AFKMPZoFwN048RC0coCT6tr00cOgQ5knVOLtR03jykYTPGzPRDsdGpZ8tA/3uIIOi76j74hCPfWF54c2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78aab620dbdf1ed46626cf4c9c59244e1a85cef3eb59575a3ffb2471447921c6","last_reissued_at":"2026-05-18T02:31:57.669602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:57.669602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Potts and random-cluster models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Geoffrey R. Grimmett","submitted_at":"2014-12-08T11:36:13Z","abstract_excerpt":"This is a short account of connections between the Tutte polynomial and the Ising, Potts, and random-cluster models. The four principal elements are the Ising model of 1925, the Tutte polynomial of 1947, the Potts model of 1952, and the random-cluster model of 1972."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2522","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1412.2522","created_at":"2026-05-18T02:31:57.669682+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.2522v1","created_at":"2026-05-18T02:31:57.669682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2522","created_at":"2026-05-18T02:31:57.669682+00:00"},{"alias_kind":"pith_short_12","alias_value":"PCVLMIG334PN","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PCVLMIG334PNIZRG","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PCVLMIG3","created_at":"2026-05-18T12:28:43.426989+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/PCVLMIG334PNIZRGZ5GJYWJEJY","json":"https://pith.science/pith/PCVLMIG334PNIZRGZ5GJYWJEJY.json","graph_json":"https://pith.science/api/pith-number/PCVLMIG334PNIZRGZ5GJYWJEJY/graph.json","events_json":"https://pith.science/api/pith-number/PCVLMIG334PNIZRGZ5GJYWJEJY/events.json","paper":"https://pith.science/paper/PCVLMIG3"},"agent_actions":{"view_html":"https://pith.science/pith/PCVLMIG334PNIZRGZ5GJYWJEJY","download_json":"https://pith.science/pith/PCVLMIG334PNIZRGZ5GJYWJEJY.json","view_paper":"https://pith.science/paper/PCVLMIG3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.2522&json=true","fetch_graph":"https://pith.science/api/pith-number/PCVLMIG334PNIZRGZ5GJYWJEJY/graph.json","fetch_events":"https://pith.science/api/pith-number/PCVLMIG334PNIZRGZ5GJYWJEJY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PCVLMIG334PNIZRGZ5GJYWJEJY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PCVLMIG334PNIZRGZ5GJYWJEJY/action/storage_attestation","attest_author":"https://pith.science/pith/PCVLMIG334PNIZRGZ5GJYWJEJY/action/author_attestation","sign_citation":"https://pith.science/pith/PCVLMIG334PNIZRGZ5GJYWJEJY/action/citation_signature","submit_replication":"https://pith.science/pith/PCVLMIG334PNIZRGZ5GJYWJEJY/action/replication_record"}},"created_at":"2026-05-18T02:31:57.669682+00:00","updated_at":"2026-05-18T02:31:57.669682+00:00"}