{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1997:QFSOYGHBP4BW2ZC6U4UAVKX4FJ","short_pith_number":"pith:QFSOYGHB","schema_version":"1.0","canonical_sha256":"8164ec18e17f036d645ea7280aaafc2a7d7a8da03e4ab72f12ef90fbc0c2b917","source":{"kind":"arxiv","id":"math/9702219","version":1},"attestation_state":"computed","paper":{"title":"The Tutte dichromate and Whitney homology of matroids","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David G. Wagner","submitted_at":"1997-02-05T00:00:00Z","abstract_excerpt":"We consider a specialization $Y_M(q,t)$ of the Tutte polynomial of a matroid $M$ which is inspired by analogy with the Potts model from statistical mechanics. The only information lost in this specialization is the number of loops of $M$. We show that the coefficients of $Y_M(1-p,t)$ are very simply related to the ranks of the Whitney homology groups of the opposite partial orders of the independent set complexes of the duals of the truncations of $M$. In particular, we obtain a new homological interpretation for the coefficients of the characteristic polynomial of a matroid."},"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":"math/9702219","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"1997-02-05T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"77f8644e63a58611c01b492c53dc746615603a652ea5f0ead6b2ccd1bda415c7","abstract_canon_sha256":"e2c4737cf7cbbab36c0a07ca4037c88639a3fab16575574850d7533e44852f68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:37.147163Z","signature_b64":"1qxZFgRtJIjWLAMCUulmVX4W0ykTqUY9XmZAapdEgRGzWGbsDUtwsM3CnqVj93/gw5znxJ0sq10xNjGCa1XbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8164ec18e17f036d645ea7280aaafc2a7d7a8da03e4ab72f12ef90fbc0c2b917","last_reissued_at":"2026-05-18T01:05:37.146648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:37.146648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Tutte dichromate and Whitney homology of matroids","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David G. Wagner","submitted_at":"1997-02-05T00:00:00Z","abstract_excerpt":"We consider a specialization $Y_M(q,t)$ of the Tutte polynomial of a matroid $M$ which is inspired by analogy with the Potts model from statistical mechanics. The only information lost in this specialization is the number of loops of $M$. We show that the coefficients of $Y_M(1-p,t)$ are very simply related to the ranks of the Whitney homology groups of the opposite partial orders of the independent set complexes of the duals of the truncations of $M$. In particular, we obtain a new homological interpretation for the coefficients of the characteristic polynomial of a matroid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9702219","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":"math/9702219","created_at":"2026-05-18T01:05:37.146724+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9702219v1","created_at":"2026-05-18T01:05:37.146724+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9702219","created_at":"2026-05-18T01:05:37.146724+00:00"},{"alias_kind":"pith_short_12","alias_value":"QFSOYGHBP4BW","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_16","alias_value":"QFSOYGHBP4BW2ZC6","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_8","alias_value":"QFSOYGHB","created_at":"2026-05-18T12:25:48.327863+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/QFSOYGHBP4BW2ZC6U4UAVKX4FJ","json":"https://pith.science/pith/QFSOYGHBP4BW2ZC6U4UAVKX4FJ.json","graph_json":"https://pith.science/api/pith-number/QFSOYGHBP4BW2ZC6U4UAVKX4FJ/graph.json","events_json":"https://pith.science/api/pith-number/QFSOYGHBP4BW2ZC6U4UAVKX4FJ/events.json","paper":"https://pith.science/paper/QFSOYGHB"},"agent_actions":{"view_html":"https://pith.science/pith/QFSOYGHBP4BW2ZC6U4UAVKX4FJ","download_json":"https://pith.science/pith/QFSOYGHBP4BW2ZC6U4UAVKX4FJ.json","view_paper":"https://pith.science/paper/QFSOYGHB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9702219&json=true","fetch_graph":"https://pith.science/api/pith-number/QFSOYGHBP4BW2ZC6U4UAVKX4FJ/graph.json","fetch_events":"https://pith.science/api/pith-number/QFSOYGHBP4BW2ZC6U4UAVKX4FJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QFSOYGHBP4BW2ZC6U4UAVKX4FJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QFSOYGHBP4BW2ZC6U4UAVKX4FJ/action/storage_attestation","attest_author":"https://pith.science/pith/QFSOYGHBP4BW2ZC6U4UAVKX4FJ/action/author_attestation","sign_citation":"https://pith.science/pith/QFSOYGHBP4BW2ZC6U4UAVKX4FJ/action/citation_signature","submit_replication":"https://pith.science/pith/QFSOYGHBP4BW2ZC6U4UAVKX4FJ/action/replication_record"}},"created_at":"2026-05-18T01:05:37.146724+00:00","updated_at":"2026-05-18T01:05:37.146724+00:00"}