{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CDW6LV3GS3XE24IBGWYVTLFODL","short_pith_number":"pith:CDW6LV3G","schema_version":"1.0","canonical_sha256":"10ede5d76696ee4d710135b159acae1ac10ae2ca9777f4b026f936c8a5c8112c","source":{"kind":"arxiv","id":"1807.11543","version":1},"attestation_state":"computed","paper":{"title":"The structure of claw-free binary matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kazuhiro Nomoto, Peter Nelson","submitted_at":"2018-07-30T19:37:23Z","abstract_excerpt":"A simple binary matroid is called claw-free if none of its rank-3 flats are independent sets. These objects can be equivalently defined as the sets $E$ of points in $\\mathrm{PG}(n-1,2)$ for which $|E \\cap P|$ is not a basis of $P$ for any plane $P$, or as the subsets $X$ of $\\mathbb{F}_2^n$ containing no linearly independent triple $x,y,z$ for which $x+y,y+z,x+z,x+y+z \\notin X$.\n  We prove a decomposition theorem that exactly determines the structure of all claw-free matroids. The theorem states that claw-free matroids either belong to one of three particular basic classes of claw-free 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":"1807.11543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T19:37:23Z","cross_cats_sorted":[],"title_canon_sha256":"da9036a454b133a76db81f54950dc0331f95cfcf0280a6ea2e43d2b479b833f1","abstract_canon_sha256":"bed8ba7c7a988c1b4f61d8700ca9d2e3eecf5f418a700d2758f3b6d94685a31c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:21.937816Z","signature_b64":"uhH8jQ1T/1A2Mhlilh/uG/KTrPZeg2Ph+CZPgaRBBar/8RAUNzBj7nyog2GJCYYgnRd9MvNlQvIQWi4+n61FBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10ede5d76696ee4d710135b159acae1ac10ae2ca9777f4b026f936c8a5c8112c","last_reissued_at":"2026-05-18T00:09:21.937255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:21.937255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The structure of claw-free binary matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kazuhiro Nomoto, Peter Nelson","submitted_at":"2018-07-30T19:37:23Z","abstract_excerpt":"A simple binary matroid is called claw-free if none of its rank-3 flats are independent sets. These objects can be equivalently defined as the sets $E$ of points in $\\mathrm{PG}(n-1,2)$ for which $|E \\cap P|$ is not a basis of $P$ for any plane $P$, or as the subsets $X$ of $\\mathbb{F}_2^n$ containing no linearly independent triple $x,y,z$ for which $x+y,y+z,x+z,x+y+z \\notin X$.\n  We prove a decomposition theorem that exactly determines the structure of all claw-free matroids. The theorem states that claw-free matroids either belong to one of three particular basic classes of claw-free matroid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11543","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":"1807.11543","created_at":"2026-05-18T00:09:21.937365+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.11543v1","created_at":"2026-05-18T00:09:21.937365+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11543","created_at":"2026-05-18T00:09:21.937365+00:00"},{"alias_kind":"pith_short_12","alias_value":"CDW6LV3GS3XE","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"CDW6LV3GS3XE24IB","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"CDW6LV3G","created_at":"2026-05-18T12:32:16.446611+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1909.02045","citing_title":"The smallest matroids with no large independent flat","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CDW6LV3GS3XE24IBGWYVTLFODL","json":"https://pith.science/pith/CDW6LV3GS3XE24IBGWYVTLFODL.json","graph_json":"https://pith.science/api/pith-number/CDW6LV3GS3XE24IBGWYVTLFODL/graph.json","events_json":"https://pith.science/api/pith-number/CDW6LV3GS3XE24IBGWYVTLFODL/events.json","paper":"https://pith.science/paper/CDW6LV3G"},"agent_actions":{"view_html":"https://pith.science/pith/CDW6LV3GS3XE24IBGWYVTLFODL","download_json":"https://pith.science/pith/CDW6LV3GS3XE24IBGWYVTLFODL.json","view_paper":"https://pith.science/paper/CDW6LV3G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.11543&json=true","fetch_graph":"https://pith.science/api/pith-number/CDW6LV3GS3XE24IBGWYVTLFODL/graph.json","fetch_events":"https://pith.science/api/pith-number/CDW6LV3GS3XE24IBGWYVTLFODL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CDW6LV3GS3XE24IBGWYVTLFODL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CDW6LV3GS3XE24IBGWYVTLFODL/action/storage_attestation","attest_author":"https://pith.science/pith/CDW6LV3GS3XE24IBGWYVTLFODL/action/author_attestation","sign_citation":"https://pith.science/pith/CDW6LV3GS3XE24IBGWYVTLFODL/action/citation_signature","submit_replication":"https://pith.science/pith/CDW6LV3GS3XE24IBGWYVTLFODL/action/replication_record"}},"created_at":"2026-05-18T00:09:21.937365+00:00","updated_at":"2026-05-18T00:09:21.937365+00:00"}