{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:66IXZ6CWVHGQH5P6BA4TIA4AIG","short_pith_number":"pith:66IXZ6CW","schema_version":"1.0","canonical_sha256":"f7917cf856a9cd03f5fe08393403804183cc1dcdd123db9e453e569b742b44f9","source":{"kind":"arxiv","id":"1002.2357","version":2},"attestation_state":"computed","paper":{"title":"Modular elimination in matroids and oriented matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emanuele Delucchi","submitted_at":"2010-02-11T15:07:39Z","abstract_excerpt":"We introduce a new axiomatization of matroid theory that requires the elimination property only among modular pairs of circuits, and we present a cryptomorphic phrasing thereof in terms of Crapo's axioms for flats. This new point of view leads to a corresponding strengthening of the circuit axioms for oriented matroids."},"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":"1002.2357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-02-11T15:07:39Z","cross_cats_sorted":[],"title_canon_sha256":"f0e5196c74084f6a23c97ed6ef58d757952f2462f36721bef1166b5c7132449a","abstract_canon_sha256":"9373294418fbccf3b2dda487c776a0d10d745d8572aedda61c302f9e05021af5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:27.726948Z","signature_b64":"OeRUU/4QM1GKyh0QvarQhASOx/i0VNQI67v4TwKGwkGjvV6R/RvwNNtgfYn1A6L2aa+RfBgJY6IspMItjOMSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7917cf856a9cd03f5fe08393403804183cc1dcdd123db9e453e569b742b44f9","last_reissued_at":"2026-05-18T01:08:27.726351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:27.726351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modular elimination in matroids and oriented matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emanuele Delucchi","submitted_at":"2010-02-11T15:07:39Z","abstract_excerpt":"We introduce a new axiomatization of matroid theory that requires the elimination property only among modular pairs of circuits, and we present a cryptomorphic phrasing thereof in terms of Crapo's axioms for flats. This new point of view leads to a corresponding strengthening of the circuit axioms for oriented matroids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2357","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":"1002.2357","created_at":"2026-05-18T01:08:27.726455+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.2357v2","created_at":"2026-05-18T01:08:27.726455+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2357","created_at":"2026-05-18T01:08:27.726455+00:00"},{"alias_kind":"pith_short_12","alias_value":"66IXZ6CWVHGQ","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"66IXZ6CWVHGQH5P6","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"66IXZ6CW","created_at":"2026-05-18T12:26:04.259169+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/66IXZ6CWVHGQH5P6BA4TIA4AIG","json":"https://pith.science/pith/66IXZ6CWVHGQH5P6BA4TIA4AIG.json","graph_json":"https://pith.science/api/pith-number/66IXZ6CWVHGQH5P6BA4TIA4AIG/graph.json","events_json":"https://pith.science/api/pith-number/66IXZ6CWVHGQH5P6BA4TIA4AIG/events.json","paper":"https://pith.science/paper/66IXZ6CW"},"agent_actions":{"view_html":"https://pith.science/pith/66IXZ6CWVHGQH5P6BA4TIA4AIG","download_json":"https://pith.science/pith/66IXZ6CWVHGQH5P6BA4TIA4AIG.json","view_paper":"https://pith.science/paper/66IXZ6CW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.2357&json=true","fetch_graph":"https://pith.science/api/pith-number/66IXZ6CWVHGQH5P6BA4TIA4AIG/graph.json","fetch_events":"https://pith.science/api/pith-number/66IXZ6CWVHGQH5P6BA4TIA4AIG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/66IXZ6CWVHGQH5P6BA4TIA4AIG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/66IXZ6CWVHGQH5P6BA4TIA4AIG/action/storage_attestation","attest_author":"https://pith.science/pith/66IXZ6CWVHGQH5P6BA4TIA4AIG/action/author_attestation","sign_citation":"https://pith.science/pith/66IXZ6CWVHGQH5P6BA4TIA4AIG/action/citation_signature","submit_replication":"https://pith.science/pith/66IXZ6CWVHGQH5P6BA4TIA4AIG/action/replication_record"}},"created_at":"2026-05-18T01:08:27.726455+00:00","updated_at":"2026-05-18T01:08:27.726455+00:00"}