{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:NFDUQVXTFVBWKDOCSXUZO4PTNP","short_pith_number":"pith:NFDUQVXT","schema_version":"1.0","canonical_sha256":"69474856f32d43650dc295e99771f36bfa0ce3343aadc8b082be10c1d18a22f8","source":{"kind":"arxiv","id":"1201.1831","version":1},"attestation_state":"computed","paper":{"title":"On Brylawski's generalized duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gary Gordon","submitted_at":"2012-01-09T16:44:36Z","abstract_excerpt":"We introduce a notion of duality (due to Brylawski) that generalizes matroid duality to arbitrary rank functions. This generalized duality allows for generalized operations (deletion and contraction) and a generalized polynomial based on the matroid Tutte polynomial. This polynomial satisfies a deletion-contraction recursion. We explore this notion of duality for greedoids, antimatroids and demi-matroids, proving that matroids correspond precisely to objects that are simultaneously greedoids and \"dual\" greedoids."},"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":"1201.1831","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-09T16:44:36Z","cross_cats_sorted":[],"title_canon_sha256":"ee07091d6f05d12cd9409d912eb657bc51ee6971e53a4ce5c96f616593ebd4bb","abstract_canon_sha256":"15468822870397aba2e36e8da6c9c6c55194cb65b994a9cb1ce361364f834e97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:55.590815Z","signature_b64":"w7qeAhehyLt930EBWiWcMses2xognSNA5SKg771Wuk9RzRFaDtdxTclVV/OTIb2egMd/H/GAeadfiJzygLtOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69474856f32d43650dc295e99771f36bfa0ce3343aadc8b082be10c1d18a22f8","last_reissued_at":"2026-05-18T04:04:55.590286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:55.590286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Brylawski's generalized duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gary Gordon","submitted_at":"2012-01-09T16:44:36Z","abstract_excerpt":"We introduce a notion of duality (due to Brylawski) that generalizes matroid duality to arbitrary rank functions. This generalized duality allows for generalized operations (deletion and contraction) and a generalized polynomial based on the matroid Tutte polynomial. This polynomial satisfies a deletion-contraction recursion. We explore this notion of duality for greedoids, antimatroids and demi-matroids, proving that matroids correspond precisely to objects that are simultaneously greedoids and \"dual\" greedoids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1831","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":"1201.1831","created_at":"2026-05-18T04:04:55.590375+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.1831v1","created_at":"2026-05-18T04:04:55.590375+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1831","created_at":"2026-05-18T04:04:55.590375+00:00"},{"alias_kind":"pith_short_12","alias_value":"NFDUQVXTFVBW","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NFDUQVXTFVBWKDOC","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NFDUQVXT","created_at":"2026-05-18T12:27:16.716162+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/NFDUQVXTFVBWKDOCSXUZO4PTNP","json":"https://pith.science/pith/NFDUQVXTFVBWKDOCSXUZO4PTNP.json","graph_json":"https://pith.science/api/pith-number/NFDUQVXTFVBWKDOCSXUZO4PTNP/graph.json","events_json":"https://pith.science/api/pith-number/NFDUQVXTFVBWKDOCSXUZO4PTNP/events.json","paper":"https://pith.science/paper/NFDUQVXT"},"agent_actions":{"view_html":"https://pith.science/pith/NFDUQVXTFVBWKDOCSXUZO4PTNP","download_json":"https://pith.science/pith/NFDUQVXTFVBWKDOCSXUZO4PTNP.json","view_paper":"https://pith.science/paper/NFDUQVXT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.1831&json=true","fetch_graph":"https://pith.science/api/pith-number/NFDUQVXTFVBWKDOCSXUZO4PTNP/graph.json","fetch_events":"https://pith.science/api/pith-number/NFDUQVXTFVBWKDOCSXUZO4PTNP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NFDUQVXTFVBWKDOCSXUZO4PTNP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NFDUQVXTFVBWKDOCSXUZO4PTNP/action/storage_attestation","attest_author":"https://pith.science/pith/NFDUQVXTFVBWKDOCSXUZO4PTNP/action/author_attestation","sign_citation":"https://pith.science/pith/NFDUQVXTFVBWKDOCSXUZO4PTNP/action/citation_signature","submit_replication":"https://pith.science/pith/NFDUQVXTFVBWKDOCSXUZO4PTNP/action/replication_record"}},"created_at":"2026-05-18T04:04:55.590375+00:00","updated_at":"2026-05-18T04:04:55.590375+00:00"}