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We also obtain other similar formulas."},"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":"0811.3463","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-11-21T04:23:17Z","cross_cats_sorted":[],"title_canon_sha256":"254d62e9acd902f6a815e13eb9edbc26856ca526448edd203e66ce4312f18009","abstract_canon_sha256":"26b3684bfea66e91e78e180b73e50aab308795c6cd946347d3278433eadf6f83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:42.821422Z","signature_b64":"xu80gAa1XdqAEDftpmZKpz6fx4QLmi+D/lDAquBOpXw4w4Ert1+ejzczOhvpAIo8m1mWNoRgHxc4w7HrAuAXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f16f5ea7895dc11d821a10349fed8f9f3beed87d5a2cbc92e0ff10b677e67bf3","last_reissued_at":"2026-05-18T04:04:42.820674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:42.820674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomiality of some hook-length statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Greta Panova","submitted_at":"2008-11-21T04:23:17Z","abstract_excerpt":"We prove a conjecture of Okada giving an exact formula for a certain statistic for hook-lengths of partitions:\n\\frac{1}{n!} \\sum_{\\lambda \\vdash n} f_{\\lambda}^2 \\sum_{u \\in \\lambda} \\prod_{i=1}^{r}(h_u^2 - i^2) = \\frac{1}{2(r+1)^2} \\binom{2r}{r}\\binom{2r+2}{r+1} \\prod_{j=0}^{r} (n-j),\nwhere $f_{\\lambda}$ is the number of standard Young tableaux of shape $\\lambda$ and $h_u$ is the hook length of the square $u$ of the Young diagram of $\\lambda$. We also obtain other similar formulas."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.3463","kind":"arxiv","version":4},"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":"0811.3463","created_at":"2026-05-18T04:04:42.820771+00:00"},{"alias_kind":"arxiv_version","alias_value":"0811.3463v4","created_at":"2026-05-18T04:04:42.820771+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.3463","created_at":"2026-05-18T04:04:42.820771+00:00"},{"alias_kind":"pith_short_12","alias_value":"6FXV5J4JLXAR","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"6FXV5J4JLXAR3AQ2","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"6FXV5J4J","created_at":"2026-05-18T12:25:56.245647+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/6FXV5J4JLXAR3AQ2CA2J73MPT4","json":"https://pith.science/pith/6FXV5J4JLXAR3AQ2CA2J73MPT4.json","graph_json":"https://pith.science/api/pith-number/6FXV5J4JLXAR3AQ2CA2J73MPT4/graph.json","events_json":"https://pith.science/api/pith-number/6FXV5J4JLXAR3AQ2CA2J73MPT4/events.json","paper":"https://pith.science/paper/6FXV5J4J"},"agent_actions":{"view_html":"https://pith.science/pith/6FXV5J4JLXAR3AQ2CA2J73MPT4","download_json":"https://pith.science/pith/6FXV5J4JLXAR3AQ2CA2J73MPT4.json","view_paper":"https://pith.science/paper/6FXV5J4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0811.3463&json=true","fetch_graph":"https://pith.science/api/pith-number/6FXV5J4JLXAR3AQ2CA2J73MPT4/graph.json","fetch_events":"https://pith.science/api/pith-number/6FXV5J4JLXAR3AQ2CA2J73MPT4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6FXV5J4JLXAR3AQ2CA2J73MPT4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6FXV5J4JLXAR3AQ2CA2J73MPT4/action/storage_attestation","attest_author":"https://pith.science/pith/6FXV5J4JLXAR3AQ2CA2J73MPT4/action/author_attestation","sign_citation":"https://pith.science/pith/6FXV5J4JLXAR3AQ2CA2J73MPT4/action/citation_signature","submit_replication":"https://pith.science/pith/6FXV5J4JLXAR3AQ2CA2J73MPT4/action/replication_record"}},"created_at":"2026-05-18T04:04:42.820771+00:00","updated_at":"2026-05-18T04:04:42.820771+00:00"}