{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KGWFP6WGDGACJP7I2GPWH5FTBK","short_pith_number":"pith:KGWFP6WG","schema_version":"1.0","canonical_sha256":"51ac57fac6198024bfe8d19f63f4b30a9b9e2c1c5b06d2d476c31d50f226724a","source":{"kind":"arxiv","id":"1409.3503","version":1},"attestation_state":"computed","paper":{"title":"Matroid theory for algebraic geometers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Eric Katz","submitted_at":"2014-09-11T17:10:23Z","abstract_excerpt":"This article is a survey of matroid theory aimed at algebraic geometers. Matroids are combinatorial abstractions of linear subspaces and hyperplane arrangements. Not all matroids come from linear subspaces; those that do are said to be representable. Still, one may apply linear algebraic constructions to non-representable matroids. There are a number of different definitions of matroids, a phenomenon known as cryptomorphism. In this survey, we begin by reviewing the classical definitions of matroids, develop operations in matroid theory, summarize some results in representability, and construc"},"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":"1409.3503","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-11T17:10:23Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3519c752a2f4c533960fef6bcb71b9dda944c096d484762c449250ee4baa57cd","abstract_canon_sha256":"f162ef83e2bfb262f1391dc8bc06952b57522f0a991a6fe6512a8e423c214d57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:01.181138Z","signature_b64":"999TZiAAfpzYVuTQ65rOiuFy9kvSMquB6r//d18BunYpkPJNTaj++dxB/7mRuEDvZO+nLk4HthqK3gafpTXGDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51ac57fac6198024bfe8d19f63f4b30a9b9e2c1c5b06d2d476c31d50f226724a","last_reissued_at":"2026-05-18T02:43:01.180695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:01.180695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matroid theory for algebraic geometers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Eric Katz","submitted_at":"2014-09-11T17:10:23Z","abstract_excerpt":"This article is a survey of matroid theory aimed at algebraic geometers. Matroids are combinatorial abstractions of linear subspaces and hyperplane arrangements. Not all matroids come from linear subspaces; those that do are said to be representable. Still, one may apply linear algebraic constructions to non-representable matroids. There are a number of different definitions of matroids, a phenomenon known as cryptomorphism. In this survey, we begin by reviewing the classical definitions of matroids, develop operations in matroid theory, summarize some results in representability, and construc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3503","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":"1409.3503","created_at":"2026-05-18T02:43:01.180761+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.3503v1","created_at":"2026-05-18T02:43:01.180761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3503","created_at":"2026-05-18T02:43:01.180761+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGWFP6WGDGAC","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGWFP6WGDGACJP7I","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGWFP6WG","created_at":"2026-05-18T12:28:35.611951+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/KGWFP6WGDGACJP7I2GPWH5FTBK","json":"https://pith.science/pith/KGWFP6WGDGACJP7I2GPWH5FTBK.json","graph_json":"https://pith.science/api/pith-number/KGWFP6WGDGACJP7I2GPWH5FTBK/graph.json","events_json":"https://pith.science/api/pith-number/KGWFP6WGDGACJP7I2GPWH5FTBK/events.json","paper":"https://pith.science/paper/KGWFP6WG"},"agent_actions":{"view_html":"https://pith.science/pith/KGWFP6WGDGACJP7I2GPWH5FTBK","download_json":"https://pith.science/pith/KGWFP6WGDGACJP7I2GPWH5FTBK.json","view_paper":"https://pith.science/paper/KGWFP6WG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.3503&json=true","fetch_graph":"https://pith.science/api/pith-number/KGWFP6WGDGACJP7I2GPWH5FTBK/graph.json","fetch_events":"https://pith.science/api/pith-number/KGWFP6WGDGACJP7I2GPWH5FTBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGWFP6WGDGACJP7I2GPWH5FTBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGWFP6WGDGACJP7I2GPWH5FTBK/action/storage_attestation","attest_author":"https://pith.science/pith/KGWFP6WGDGACJP7I2GPWH5FTBK/action/author_attestation","sign_citation":"https://pith.science/pith/KGWFP6WGDGACJP7I2GPWH5FTBK/action/citation_signature","submit_replication":"https://pith.science/pith/KGWFP6WGDGACJP7I2GPWH5FTBK/action/replication_record"}},"created_at":"2026-05-18T02:43:01.180761+00:00","updated_at":"2026-05-18T02:43:01.180761+00:00"}