{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JCKQBKHRGJ44PD7REA7A4QX5JX","short_pith_number":"pith:JCKQBKHR","schema_version":"1.0","canonical_sha256":"489500a8f13279c78ff1203e0e42fd4de12d19583b841417f97444312f5f2196","source":{"kind":"arxiv","id":"1904.00543","version":2},"attestation_state":"computed","paper":{"title":"A combinatorial proof of the supper symmetric property of hook length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Masanori Ando","submitted_at":"2019-04-01T02:55:29Z","abstract_excerpt":"There are $k$ kinds of length $k$ hooks with different arm length. Actually, this $k$ kinds appear uniformly in Young diagrams of size $n$. The property ``appear uniformly'' is called super symmetric. We give a combinatorial proof of the supper symmetric property of hook length."},"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":"1904.00543","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-01T02:55:29Z","cross_cats_sorted":[],"title_canon_sha256":"393ce430c768d3652fb043f4a3229bc11eda400f125f6669df43562ce3979388","abstract_canon_sha256":"1f484fcb1910baef7bf29f52e34c00bfab9c977769cd46a1cbfefbdb3573e0fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:08.609025Z","signature_b64":"/NPbHp/ye8iCWOhNG5WhfrpgpwrFg3YfNzfKBvECnU0Ru4ikAvhv+3BrfrkN6So4Q9t7FjEVLbnjD90fKggFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"489500a8f13279c78ff1203e0e42fd4de12d19583b841417f97444312f5f2196","last_reissued_at":"2026-05-17T23:49:08.608391Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:08.608391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A combinatorial proof of the supper symmetric property of hook length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Masanori Ando","submitted_at":"2019-04-01T02:55:29Z","abstract_excerpt":"There are $k$ kinds of length $k$ hooks with different arm length. Actually, this $k$ kinds appear uniformly in Young diagrams of size $n$. The property ``appear uniformly'' is called super symmetric. We give a combinatorial proof of the supper symmetric property of hook length."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00543","kind":"arxiv","version":2},"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":"1904.00543","created_at":"2026-05-17T23:49:08.608489+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.00543v2","created_at":"2026-05-17T23:49:08.608489+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00543","created_at":"2026-05-17T23:49:08.608489+00:00"},{"alias_kind":"pith_short_12","alias_value":"JCKQBKHRGJ44","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"JCKQBKHRGJ44PD7R","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"JCKQBKHR","created_at":"2026-05-18T12:33:18.533446+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/JCKQBKHRGJ44PD7REA7A4QX5JX","json":"https://pith.science/pith/JCKQBKHRGJ44PD7REA7A4QX5JX.json","graph_json":"https://pith.science/api/pith-number/JCKQBKHRGJ44PD7REA7A4QX5JX/graph.json","events_json":"https://pith.science/api/pith-number/JCKQBKHRGJ44PD7REA7A4QX5JX/events.json","paper":"https://pith.science/paper/JCKQBKHR"},"agent_actions":{"view_html":"https://pith.science/pith/JCKQBKHRGJ44PD7REA7A4QX5JX","download_json":"https://pith.science/pith/JCKQBKHRGJ44PD7REA7A4QX5JX.json","view_paper":"https://pith.science/paper/JCKQBKHR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.00543&json=true","fetch_graph":"https://pith.science/api/pith-number/JCKQBKHRGJ44PD7REA7A4QX5JX/graph.json","fetch_events":"https://pith.science/api/pith-number/JCKQBKHRGJ44PD7REA7A4QX5JX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JCKQBKHRGJ44PD7REA7A4QX5JX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JCKQBKHRGJ44PD7REA7A4QX5JX/action/storage_attestation","attest_author":"https://pith.science/pith/JCKQBKHRGJ44PD7REA7A4QX5JX/action/author_attestation","sign_citation":"https://pith.science/pith/JCKQBKHRGJ44PD7REA7A4QX5JX/action/citation_signature","submit_replication":"https://pith.science/pith/JCKQBKHRGJ44PD7REA7A4QX5JX/action/replication_record"}},"created_at":"2026-05-17T23:49:08.608489+00:00","updated_at":"2026-05-17T23:49:08.608489+00:00"}