{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NQP7U4VGCWEPNPW7KJ3BV4JHOT","short_pith_number":"pith:NQP7U4VG","schema_version":"1.0","canonical_sha256":"6c1ffa72a61588f6bedf52761af12774c7f85f1ad8723a3dd7a0a3e1aa2ff52e","source":{"kind":"arxiv","id":"1310.8378","version":1},"attestation_state":"computed","paper":{"title":"Stanley-Wilf limits are typically exponential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jacob Fox","submitted_at":"2013-10-31T04:25:37Z","abstract_excerpt":"For a permutation $\\pi$, let $S_{n}(\\pi)$ be the number of permutations on $n$ letters avoiding $\\pi$. Marcus and Tardos proved the celebrated Stanley-Wilf conjecture that $L(\\pi)= \\lim_{n \\to \\infty} S_n(\\pi)^{1/n}$ exists and is finite. Backed by numerical evidence, it has been conjectured by many researchers over the years that $L(\\pi)=\\Theta(k^2)$ for every permutation $\\pi$ on $k$ letters. We disprove this conjecture, showing that $L(\\pi)=2^{k^{\\Theta(1)}}$ for almost all permutations $\\pi$ on $k$ letters."},"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":"1310.8378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-31T04:25:37Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"53d8ebd6d829ab55199e861bbc269afaf78ee03e77df1070f4548eafe6cd8efe","abstract_canon_sha256":"8322e9b038b3771b2a686b67105134e4630491d70f0403b829d3af5140336c9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:17.284509Z","signature_b64":"P7Xe2aAlSLEk3SsAnC0DkoNJdNcm+rNOy8sW6W809MWgWuZoRFtGCT/CkH8G8beEJmJPxJbSTG1vJXwCw7coBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c1ffa72a61588f6bedf52761af12774c7f85f1ad8723a3dd7a0a3e1aa2ff52e","last_reissued_at":"2026-05-18T03:08:17.283952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:17.283952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stanley-Wilf limits are typically exponential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jacob Fox","submitted_at":"2013-10-31T04:25:37Z","abstract_excerpt":"For a permutation $\\pi$, let $S_{n}(\\pi)$ be the number of permutations on $n$ letters avoiding $\\pi$. Marcus and Tardos proved the celebrated Stanley-Wilf conjecture that $L(\\pi)= \\lim_{n \\to \\infty} S_n(\\pi)^{1/n}$ exists and is finite. Backed by numerical evidence, it has been conjectured by many researchers over the years that $L(\\pi)=\\Theta(k^2)$ for every permutation $\\pi$ on $k$ letters. We disprove this conjecture, showing that $L(\\pi)=2^{k^{\\Theta(1)}}$ for almost all permutations $\\pi$ on $k$ letters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8378","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":"1310.8378","created_at":"2026-05-18T03:08:17.284039+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.8378v1","created_at":"2026-05-18T03:08:17.284039+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8378","created_at":"2026-05-18T03:08:17.284039+00:00"},{"alias_kind":"pith_short_12","alias_value":"NQP7U4VGCWEP","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NQP7U4VGCWEPNPW7","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NQP7U4VG","created_at":"2026-05-18T12:27:52.871228+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2601.05166","citing_title":"Inapproximability of Counting Permutation Patterns","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NQP7U4VGCWEPNPW7KJ3BV4JHOT","json":"https://pith.science/pith/NQP7U4VGCWEPNPW7KJ3BV4JHOT.json","graph_json":"https://pith.science/api/pith-number/NQP7U4VGCWEPNPW7KJ3BV4JHOT/graph.json","events_json":"https://pith.science/api/pith-number/NQP7U4VGCWEPNPW7KJ3BV4JHOT/events.json","paper":"https://pith.science/paper/NQP7U4VG"},"agent_actions":{"view_html":"https://pith.science/pith/NQP7U4VGCWEPNPW7KJ3BV4JHOT","download_json":"https://pith.science/pith/NQP7U4VGCWEPNPW7KJ3BV4JHOT.json","view_paper":"https://pith.science/paper/NQP7U4VG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.8378&json=true","fetch_graph":"https://pith.science/api/pith-number/NQP7U4VGCWEPNPW7KJ3BV4JHOT/graph.json","fetch_events":"https://pith.science/api/pith-number/NQP7U4VGCWEPNPW7KJ3BV4JHOT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NQP7U4VGCWEPNPW7KJ3BV4JHOT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NQP7U4VGCWEPNPW7KJ3BV4JHOT/action/storage_attestation","attest_author":"https://pith.science/pith/NQP7U4VGCWEPNPW7KJ3BV4JHOT/action/author_attestation","sign_citation":"https://pith.science/pith/NQP7U4VGCWEPNPW7KJ3BV4JHOT/action/citation_signature","submit_replication":"https://pith.science/pith/NQP7U4VGCWEPNPW7KJ3BV4JHOT/action/replication_record"}},"created_at":"2026-05-18T03:08:17.284039+00:00","updated_at":"2026-05-18T03:08:17.284039+00:00"}