{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:X5URLFTDYR6UOHIZ7S7J2P5QSW","short_pith_number":"pith:X5URLFTD","schema_version":"1.0","canonical_sha256":"bf69159663c47d471d19fcbe9d3fb095883563118082bfadbd4eec5d6f9e6d81","source":{"kind":"arxiv","id":"1206.6270","version":5},"attestation_state":"computed","paper":{"title":"On the number of matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J.G. van der Pol, N. Bansal, R.A. Pendavingh","submitted_at":"2012-06-27T14:09:16Z","abstract_excerpt":"We consider the problem of determining $m_n$, the number of matroids on $n$ elements. The best known lower bound on $m_n$ is due to Knuth (1974) who showed that $\\log \\log m_n$ is at least $n-3/2\\log n-1$. On the other hand, Piff (1973) showed that $\\log\\log m_n\\leq n-\\log n+\\log\\log n +O(1)$, and it has been conjectured since that the right answer is perhaps closer to Knuth's bound.\n  We show that this is indeed the case, and prove an upper bound on $\\log\\log m_n$ that is within an additive $1+o(1)$ term of Knuth's lower bound. Our proof is based on using some structural properties of non-bas"},"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":"1206.6270","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-27T14:09:16Z","cross_cats_sorted":[],"title_canon_sha256":"570d698f9fc80e645d8d013131a3f584c284d9aaa5c2e57e9c702d124ea0b729","abstract_canon_sha256":"937290c11c4c2fd9f4f70c390fa564553c597c21ab8ddd4fe0576248bbb8cc30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:33.354673Z","signature_b64":"9p+RW0oJY+HfYhD1aItQYO4bGWECfKGH3fgtmrtLWYnyNn7YkECDCj+T5kFJhwmMKKdEFJ/APi/rnV1yMhUTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf69159663c47d471d19fcbe9d3fb095883563118082bfadbd4eec5d6f9e6d81","last_reissued_at":"2026-05-18T03:12:33.353975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:33.353975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the number of matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J.G. van der Pol, N. Bansal, R.A. Pendavingh","submitted_at":"2012-06-27T14:09:16Z","abstract_excerpt":"We consider the problem of determining $m_n$, the number of matroids on $n$ elements. The best known lower bound on $m_n$ is due to Knuth (1974) who showed that $\\log \\log m_n$ is at least $n-3/2\\log n-1$. On the other hand, Piff (1973) showed that $\\log\\log m_n\\leq n-\\log n+\\log\\log n +O(1)$, and it has been conjectured since that the right answer is perhaps closer to Knuth's bound.\n  We show that this is indeed the case, and prove an upper bound on $\\log\\log m_n$ that is within an additive $1+o(1)$ term of Knuth's lower bound. Our proof is based on using some structural properties of non-bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6270","kind":"arxiv","version":5},"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":"1206.6270","created_at":"2026-05-18T03:12:33.354089+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.6270v5","created_at":"2026-05-18T03:12:33.354089+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6270","created_at":"2026-05-18T03:12:33.354089+00:00"},{"alias_kind":"pith_short_12","alias_value":"X5URLFTDYR6U","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"X5URLFTDYR6UOHIZ","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"X5URLFTD","created_at":"2026-05-18T12:27:27.928770+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/X5URLFTDYR6UOHIZ7S7J2P5QSW","json":"https://pith.science/pith/X5URLFTDYR6UOHIZ7S7J2P5QSW.json","graph_json":"https://pith.science/api/pith-number/X5URLFTDYR6UOHIZ7S7J2P5QSW/graph.json","events_json":"https://pith.science/api/pith-number/X5URLFTDYR6UOHIZ7S7J2P5QSW/events.json","paper":"https://pith.science/paper/X5URLFTD"},"agent_actions":{"view_html":"https://pith.science/pith/X5URLFTDYR6UOHIZ7S7J2P5QSW","download_json":"https://pith.science/pith/X5URLFTDYR6UOHIZ7S7J2P5QSW.json","view_paper":"https://pith.science/paper/X5URLFTD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.6270&json=true","fetch_graph":"https://pith.science/api/pith-number/X5URLFTDYR6UOHIZ7S7J2P5QSW/graph.json","fetch_events":"https://pith.science/api/pith-number/X5URLFTDYR6UOHIZ7S7J2P5QSW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X5URLFTDYR6UOHIZ7S7J2P5QSW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X5URLFTDYR6UOHIZ7S7J2P5QSW/action/storage_attestation","attest_author":"https://pith.science/pith/X5URLFTDYR6UOHIZ7S7J2P5QSW/action/author_attestation","sign_citation":"https://pith.science/pith/X5URLFTDYR6UOHIZ7S7J2P5QSW/action/citation_signature","submit_replication":"https://pith.science/pith/X5URLFTDYR6UOHIZ7S7J2P5QSW/action/replication_record"}},"created_at":"2026-05-18T03:12:33.354089+00:00","updated_at":"2026-05-18T03:12:33.354089+00:00"}