{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:DIWVNKWNLXJOVD3PWJTGIQQU55","short_pith_number":"pith:DIWVNKWN","schema_version":"1.0","canonical_sha256":"1a2d56aacd5dd2ea8f6fb266644214ef425d2d2166a863111907c9c44684802f","source":{"kind":"arxiv","id":"1101.4691","version":1},"attestation_state":"computed","paper":{"title":"Certifying Non-representability of Matroids Over Prime Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geoff Whittle, Jim Geelen","submitted_at":"2011-01-25T00:12:34Z","abstract_excerpt":"It is proved that, for a prime number $p$, showing that an $n$-element matroid is not representable over $GF(p)$ requires only $O(n^2)$ rank evaluations."},"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":"1101.4691","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-25T00:12:34Z","cross_cats_sorted":[],"title_canon_sha256":"167ee1567faa4b04626cdbf8768cf62311f552af01bdf3adc819158718900a1e","abstract_canon_sha256":"b88c7c4d79efc348331fdb0af130f834d1e71f5295fe2ccd92fcbf5f8fbb4c80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:59.200599Z","signature_b64":"BTF+lNmklgCoj02UlHd3a2QPIpjyovlRfERouB1NguPBSmxH4gxtFb64MawGB+3kmDEQSfllstZDm8yGybBjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a2d56aacd5dd2ea8f6fb266644214ef425d2d2166a863111907c9c44684802f","last_reissued_at":"2026-05-18T04:30:59.199916Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:59.199916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Certifying Non-representability of Matroids Over Prime Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geoff Whittle, Jim Geelen","submitted_at":"2011-01-25T00:12:34Z","abstract_excerpt":"It is proved that, for a prime number $p$, showing that an $n$-element matroid is not representable over $GF(p)$ requires only $O(n^2)$ rank evaluations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4691","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":"1101.4691","created_at":"2026-05-18T04:30:59.200029+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.4691v1","created_at":"2026-05-18T04:30:59.200029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4691","created_at":"2026-05-18T04:30:59.200029+00:00"},{"alias_kind":"pith_short_12","alias_value":"DIWVNKWNLXJO","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DIWVNKWNLXJOVD3P","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DIWVNKWN","created_at":"2026-05-18T12:26:26.731475+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/DIWVNKWNLXJOVD3PWJTGIQQU55","json":"https://pith.science/pith/DIWVNKWNLXJOVD3PWJTGIQQU55.json","graph_json":"https://pith.science/api/pith-number/DIWVNKWNLXJOVD3PWJTGIQQU55/graph.json","events_json":"https://pith.science/api/pith-number/DIWVNKWNLXJOVD3PWJTGIQQU55/events.json","paper":"https://pith.science/paper/DIWVNKWN"},"agent_actions":{"view_html":"https://pith.science/pith/DIWVNKWNLXJOVD3PWJTGIQQU55","download_json":"https://pith.science/pith/DIWVNKWNLXJOVD3PWJTGIQQU55.json","view_paper":"https://pith.science/paper/DIWVNKWN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.4691&json=true","fetch_graph":"https://pith.science/api/pith-number/DIWVNKWNLXJOVD3PWJTGIQQU55/graph.json","fetch_events":"https://pith.science/api/pith-number/DIWVNKWNLXJOVD3PWJTGIQQU55/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DIWVNKWNLXJOVD3PWJTGIQQU55/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DIWVNKWNLXJOVD3PWJTGIQQU55/action/storage_attestation","attest_author":"https://pith.science/pith/DIWVNKWNLXJOVD3PWJTGIQQU55/action/author_attestation","sign_citation":"https://pith.science/pith/DIWVNKWNLXJOVD3PWJTGIQQU55/action/citation_signature","submit_replication":"https://pith.science/pith/DIWVNKWNLXJOVD3PWJTGIQQU55/action/replication_record"}},"created_at":"2026-05-18T04:30:59.200029+00:00","updated_at":"2026-05-18T04:30:59.200029+00:00"}