{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:Z7HGIQTWIAYFWYMVP3QNF7YANZ","short_pith_number":"pith:Z7HGIQTW","schema_version":"1.0","canonical_sha256":"cfce64427640305b61957ee0d2ff006e7b6b8228278029329020ad32854e5f0d","source":{"kind":"arxiv","id":"math/0610640","version":2},"attestation_state":"computed","paper":{"title":"Factorizations of permutations into star transpositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amarpreet Rattan, John Irving","submitted_at":"2006-10-21T00:00:38Z","abstract_excerpt":"We give a compact expression for the number of factorizations of any permutation into a minimal number of transpositions of the form $(1 i)$. Our result generalizes earlier work of Pak in which substantial restrictions were placed on the permutation being factored."},"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":"math/0610640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2006-10-21T00:00:38Z","cross_cats_sorted":[],"title_canon_sha256":"dd2b8a9f77f7fe7ace94f2d8eb07ea208e79b0a7f860b23ebaa79a76375fa238","abstract_canon_sha256":"28daa65e94707443ea720790eb3a951f70e6d19b75191c64c3d68e1b0bed63d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:25.808239Z","signature_b64":"Ig49AFKJ+JsYYz9+5VmPZUdWz02sPppyChLTWsPibvxQtaUPSyLXHROVGBbSX557AAV3rYqHl8KZQiT0r1dgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfce64427640305b61957ee0d2ff006e7b6b8228278029329020ad32854e5f0d","last_reissued_at":"2026-05-18T02:51:25.807614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:25.807614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Factorizations of permutations into star transpositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amarpreet Rattan, John Irving","submitted_at":"2006-10-21T00:00:38Z","abstract_excerpt":"We give a compact expression for the number of factorizations of any permutation into a minimal number of transpositions of the form $(1 i)$. Our result generalizes earlier work of Pak in which substantial restrictions were placed on the permutation being factored."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610640","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":"math/0610640","created_at":"2026-05-18T02:51:25.807708+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0610640v2","created_at":"2026-05-18T02:51:25.807708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0610640","created_at":"2026-05-18T02:51:25.807708+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z7HGIQTWIAYF","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z7HGIQTWIAYFWYMV","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z7HGIQTW","created_at":"2026-05-18T12:25:54.717736+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/Z7HGIQTWIAYFWYMVP3QNF7YANZ","json":"https://pith.science/pith/Z7HGIQTWIAYFWYMVP3QNF7YANZ.json","graph_json":"https://pith.science/api/pith-number/Z7HGIQTWIAYFWYMVP3QNF7YANZ/graph.json","events_json":"https://pith.science/api/pith-number/Z7HGIQTWIAYFWYMVP3QNF7YANZ/events.json","paper":"https://pith.science/paper/Z7HGIQTW"},"agent_actions":{"view_html":"https://pith.science/pith/Z7HGIQTWIAYFWYMVP3QNF7YANZ","download_json":"https://pith.science/pith/Z7HGIQTWIAYFWYMVP3QNF7YANZ.json","view_paper":"https://pith.science/paper/Z7HGIQTW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0610640&json=true","fetch_graph":"https://pith.science/api/pith-number/Z7HGIQTWIAYFWYMVP3QNF7YANZ/graph.json","fetch_events":"https://pith.science/api/pith-number/Z7HGIQTWIAYFWYMVP3QNF7YANZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z7HGIQTWIAYFWYMVP3QNF7YANZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z7HGIQTWIAYFWYMVP3QNF7YANZ/action/storage_attestation","attest_author":"https://pith.science/pith/Z7HGIQTWIAYFWYMVP3QNF7YANZ/action/author_attestation","sign_citation":"https://pith.science/pith/Z7HGIQTWIAYFWYMVP3QNF7YANZ/action/citation_signature","submit_replication":"https://pith.science/pith/Z7HGIQTWIAYFWYMVP3QNF7YANZ/action/replication_record"}},"created_at":"2026-05-18T02:51:25.807708+00:00","updated_at":"2026-05-18T02:51:25.807708+00:00"}