{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:5LZDZWHI5WWPDXDC5FCD4OCSA2","short_pith_number":"pith:5LZDZWHI","schema_version":"1.0","canonical_sha256":"eaf23cd8e8edacf1dc62e9443e3852068fbaaaaaade0a99278d997cb8ea70997","source":{"kind":"arxiv","id":"1311.6742","version":3},"attestation_state":"computed","paper":{"title":"Random generators of the symmetric group: diameter, mixing time and spectral gap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.GR","authors_text":"\\'Akos Seress, Andrzej Zuk, Harald A. Helfgott","submitted_at":"2013-11-26T17:18:50Z","abstract_excerpt":"Let $g$, $h$ be a random pair of generators of $G=Sym(n)$ or $G=Alt(n)$. We show that, with probability tending to $1$ as $n\\to \\infty$, (a) the diameter of $G$ with respect to $S = \\{g,h,g^{-1},h^{-1}\\}$ is at most $O(n^2 (\\log n)^c)$, and (b) the mixing time of $G$ with respect to $S$ is at most $O(n^3 (\\log n)^c)$. (Both $c$ and the implied constants are absolute.)\n  These bounds are far lower than the strongest worst-case bounds known (in Helfgott--Seress, 2013); they roughly match the worst known examples. We also give an improved, though still non-constant, bound on the spectral gap.\n  O"},"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":"1311.6742","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-26T17:18:50Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"670744a47a700391af88995c53428fb3317bba397c26090ea53bf7a3fb2fa832","abstract_canon_sha256":"4d471d171190ddc6eb28abdf1228b88bb5a579c57663851375826aad150d66f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:45.048159Z","signature_b64":"qDuDBOYSnTiwbkCji3ASEiSXh7yLVw6VZTWloOakud3QCilPbApuACw4egWLDSaCq/D41EZXFfp/r+HUOUnhAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eaf23cd8e8edacf1dc62e9443e3852068fbaaaaaade0a99278d997cb8ea70997","last_reissued_at":"2026-05-18T02:56:45.047661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:45.047661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random generators of the symmetric group: diameter, mixing time and spectral gap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.GR","authors_text":"\\'Akos Seress, Andrzej Zuk, Harald A. Helfgott","submitted_at":"2013-11-26T17:18:50Z","abstract_excerpt":"Let $g$, $h$ be a random pair of generators of $G=Sym(n)$ or $G=Alt(n)$. We show that, with probability tending to $1$ as $n\\to \\infty$, (a) the diameter of $G$ with respect to $S = \\{g,h,g^{-1},h^{-1}\\}$ is at most $O(n^2 (\\log n)^c)$, and (b) the mixing time of $G$ with respect to $S$ is at most $O(n^3 (\\log n)^c)$. (Both $c$ and the implied constants are absolute.)\n  These bounds are far lower than the strongest worst-case bounds known (in Helfgott--Seress, 2013); they roughly match the worst known examples. We also give an improved, though still non-constant, bound on the spectral gap.\n  O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6742","kind":"arxiv","version":3},"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":"1311.6742","created_at":"2026-05-18T02:56:45.047737+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.6742v3","created_at":"2026-05-18T02:56:45.047737+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6742","created_at":"2026-05-18T02:56:45.047737+00:00"},{"alias_kind":"pith_short_12","alias_value":"5LZDZWHI5WWP","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"5LZDZWHI5WWPDXDC","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"5LZDZWHI","created_at":"2026-05-18T12:27:34.582898+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/5LZDZWHI5WWPDXDC5FCD4OCSA2","json":"https://pith.science/pith/5LZDZWHI5WWPDXDC5FCD4OCSA2.json","graph_json":"https://pith.science/api/pith-number/5LZDZWHI5WWPDXDC5FCD4OCSA2/graph.json","events_json":"https://pith.science/api/pith-number/5LZDZWHI5WWPDXDC5FCD4OCSA2/events.json","paper":"https://pith.science/paper/5LZDZWHI"},"agent_actions":{"view_html":"https://pith.science/pith/5LZDZWHI5WWPDXDC5FCD4OCSA2","download_json":"https://pith.science/pith/5LZDZWHI5WWPDXDC5FCD4OCSA2.json","view_paper":"https://pith.science/paper/5LZDZWHI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.6742&json=true","fetch_graph":"https://pith.science/api/pith-number/5LZDZWHI5WWPDXDC5FCD4OCSA2/graph.json","fetch_events":"https://pith.science/api/pith-number/5LZDZWHI5WWPDXDC5FCD4OCSA2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5LZDZWHI5WWPDXDC5FCD4OCSA2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5LZDZWHI5WWPDXDC5FCD4OCSA2/action/storage_attestation","attest_author":"https://pith.science/pith/5LZDZWHI5WWPDXDC5FCD4OCSA2/action/author_attestation","sign_citation":"https://pith.science/pith/5LZDZWHI5WWPDXDC5FCD4OCSA2/action/citation_signature","submit_replication":"https://pith.science/pith/5LZDZWHI5WWPDXDC5FCD4OCSA2/action/replication_record"}},"created_at":"2026-05-18T02:56:45.047737+00:00","updated_at":"2026-05-18T02:56:45.047737+00:00"}