{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6Q5ZLOBIBBCNGQ2FE3345N2E5D","short_pith_number":"pith:6Q5ZLOBI","schema_version":"1.0","canonical_sha256":"f43b95b8280844d3434526f7ceb744e8f4d4c5eec90326f766a04d9ddfe35219","source":{"kind":"arxiv","id":"1207.2759","version":2},"attestation_state":"computed","paper":{"title":"Principal minors Pfaffian half-tree theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"B\\'eatrice de Tili\\`ere","submitted_at":"2012-07-11T19:56:02Z","abstract_excerpt":"A half-tree is an edge configuration whose superimposition with a perfect matching is a tree. In this paper, we prove a half-tree theorem for the Pfaffian principal minors of a skew-symmetric matrix whose column sum is zero; introducing an explicit algorithm, we fully characterize half-trees involved. This question naturally arose in the context of statistical mechanics where we aimed at relating perfect matchings and trees on the same graph. As a consequence of the Pfaffian half-tree theorem, we obtain a refined version of the matrix-tree theorem in the case of skew-symmetric matrices, as wel"},"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":"1207.2759","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-11T19:56:02Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"09280dc56b28a988e98d941ba6f9775b8071dc2ea271328b68041bbe3a146229","abstract_canon_sha256":"feca687ca778c837abb42a833b02f54282f07e1052063949b7369cec57f65545"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:47.052705Z","signature_b64":"vsfIhge7LFdRnwLTD7uijQn+ufIDG/eWfKK2xc6UANh6jyfrVJbiss10UsJgKAj71BuTsUTww4uPXtA2xv5UAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f43b95b8280844d3434526f7ceb744e8f4d4c5eec90326f766a04d9ddfe35219","last_reissued_at":"2026-05-18T03:01:47.051968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:47.051968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Principal minors Pfaffian half-tree theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"B\\'eatrice de Tili\\`ere","submitted_at":"2012-07-11T19:56:02Z","abstract_excerpt":"A half-tree is an edge configuration whose superimposition with a perfect matching is a tree. In this paper, we prove a half-tree theorem for the Pfaffian principal minors of a skew-symmetric matrix whose column sum is zero; introducing an explicit algorithm, we fully characterize half-trees involved. This question naturally arose in the context of statistical mechanics where we aimed at relating perfect matchings and trees on the same graph. As a consequence of the Pfaffian half-tree theorem, we obtain a refined version of the matrix-tree theorem in the case of skew-symmetric matrices, as wel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2759","kind":"arxiv","version":2},"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":"1207.2759","created_at":"2026-05-18T03:01:47.052093+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.2759v2","created_at":"2026-05-18T03:01:47.052093+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2759","created_at":"2026-05-18T03:01:47.052093+00:00"},{"alias_kind":"pith_short_12","alias_value":"6Q5ZLOBIBBCN","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6Q5ZLOBIBBCNGQ2F","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6Q5ZLOBI","created_at":"2026-05-18T12:26:56.085431+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/6Q5ZLOBIBBCNGQ2FE3345N2E5D","json":"https://pith.science/pith/6Q5ZLOBIBBCNGQ2FE3345N2E5D.json","graph_json":"https://pith.science/api/pith-number/6Q5ZLOBIBBCNGQ2FE3345N2E5D/graph.json","events_json":"https://pith.science/api/pith-number/6Q5ZLOBIBBCNGQ2FE3345N2E5D/events.json","paper":"https://pith.science/paper/6Q5ZLOBI"},"agent_actions":{"view_html":"https://pith.science/pith/6Q5ZLOBIBBCNGQ2FE3345N2E5D","download_json":"https://pith.science/pith/6Q5ZLOBIBBCNGQ2FE3345N2E5D.json","view_paper":"https://pith.science/paper/6Q5ZLOBI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.2759&json=true","fetch_graph":"https://pith.science/api/pith-number/6Q5ZLOBIBBCNGQ2FE3345N2E5D/graph.json","fetch_events":"https://pith.science/api/pith-number/6Q5ZLOBIBBCNGQ2FE3345N2E5D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6Q5ZLOBIBBCNGQ2FE3345N2E5D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6Q5ZLOBIBBCNGQ2FE3345N2E5D/action/storage_attestation","attest_author":"https://pith.science/pith/6Q5ZLOBIBBCNGQ2FE3345N2E5D/action/author_attestation","sign_citation":"https://pith.science/pith/6Q5ZLOBIBBCNGQ2FE3345N2E5D/action/citation_signature","submit_replication":"https://pith.science/pith/6Q5ZLOBIBBCNGQ2FE3345N2E5D/action/replication_record"}},"created_at":"2026-05-18T03:01:47.052093+00:00","updated_at":"2026-05-18T03:01:47.052093+00:00"}