{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZSYMNQYIP4RNJIE3KTNNTQEC6T","short_pith_number":"pith:ZSYMNQYI","schema_version":"1.0","canonical_sha256":"ccb0c6c3087f22d4a09b54dad9c082f4e795e868d64ec41be9c8b3ab5b0dcc3e","source":{"kind":"arxiv","id":"1305.2956","version":1},"attestation_state":"computed","paper":{"title":"Mathematical structure of three - dimensional (3D) Ising model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Zhi-dong Zhang","submitted_at":"2013-05-10T01:47:05Z","abstract_excerpt":"An overview of the mathematical structure of the three-dimensional (3D) Ising model is given, from the viewpoints of topologic, algebraic and geometric aspects. By analyzing the relations among transfer matrices of the 3D Ising model, Reidemeister moves in the knot theory, Yang-Baxter and tetrahedron equations, the following facts are illustrated for the 3D Ising model: 1) The complexified quaternion basis constructed for the 3D Ising model represents naturally the rotation in a (3 + 1) - dimensional space-time, as a relativistic quantum statistical mechanics model, which is consistent with 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":"1305.2956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2013-05-10T01:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"1fcdc1e9192ba61ac9f13ca1beaf99be0b82cda31ea5c7b1c16d45803a06daea","abstract_canon_sha256":"c1ff8b3e14b7ed0b8612dcf3df65bdb19761e1d4850d941a35829892a4dfaac4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:45.376523Z","signature_b64":"YO6m4Opq7vvFpnyxDFQKMMRoey+cbB0hx1vY+9XtBLLcY2BPYybEmQ9s+RDmHJqwQurYER1U5o6eohnOKZb9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccb0c6c3087f22d4a09b54dad9c082f4e795e868d64ec41be9c8b3ab5b0dcc3e","last_reissued_at":"2026-05-18T03:25:45.375723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:45.375723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mathematical structure of three - dimensional (3D) Ising model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Zhi-dong Zhang","submitted_at":"2013-05-10T01:47:05Z","abstract_excerpt":"An overview of the mathematical structure of the three-dimensional (3D) Ising model is given, from the viewpoints of topologic, algebraic and geometric aspects. By analyzing the relations among transfer matrices of the 3D Ising model, Reidemeister moves in the knot theory, Yang-Baxter and tetrahedron equations, the following facts are illustrated for the 3D Ising model: 1) The complexified quaternion basis constructed for the 3D Ising model represents naturally the rotation in a (3 + 1) - dimensional space-time, as a relativistic quantum statistical mechanics model, which is consistent with th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2956","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":"1305.2956","created_at":"2026-05-18T03:25:45.375846+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.2956v1","created_at":"2026-05-18T03:25:45.375846+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2956","created_at":"2026-05-18T03:25:45.375846+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZSYMNQYIP4RN","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZSYMNQYIP4RNJIE3","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZSYMNQYI","created_at":"2026-05-18T12:28:09.283467+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/ZSYMNQYIP4RNJIE3KTNNTQEC6T","json":"https://pith.science/pith/ZSYMNQYIP4RNJIE3KTNNTQEC6T.json","graph_json":"https://pith.science/api/pith-number/ZSYMNQYIP4RNJIE3KTNNTQEC6T/graph.json","events_json":"https://pith.science/api/pith-number/ZSYMNQYIP4RNJIE3KTNNTQEC6T/events.json","paper":"https://pith.science/paper/ZSYMNQYI"},"agent_actions":{"view_html":"https://pith.science/pith/ZSYMNQYIP4RNJIE3KTNNTQEC6T","download_json":"https://pith.science/pith/ZSYMNQYIP4RNJIE3KTNNTQEC6T.json","view_paper":"https://pith.science/paper/ZSYMNQYI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.2956&json=true","fetch_graph":"https://pith.science/api/pith-number/ZSYMNQYIP4RNJIE3KTNNTQEC6T/graph.json","fetch_events":"https://pith.science/api/pith-number/ZSYMNQYIP4RNJIE3KTNNTQEC6T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZSYMNQYIP4RNJIE3KTNNTQEC6T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZSYMNQYIP4RNJIE3KTNNTQEC6T/action/storage_attestation","attest_author":"https://pith.science/pith/ZSYMNQYIP4RNJIE3KTNNTQEC6T/action/author_attestation","sign_citation":"https://pith.science/pith/ZSYMNQYIP4RNJIE3KTNNTQEC6T/action/citation_signature","submit_replication":"https://pith.science/pith/ZSYMNQYIP4RNJIE3KTNNTQEC6T/action/replication_record"}},"created_at":"2026-05-18T03:25:45.375846+00:00","updated_at":"2026-05-18T03:25:45.375846+00:00"}