{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6UTOODF7RP5CNGPXXJEM3UB5X5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"81edacd4717492adce26b0e237489a0ae3cdce6103db21075b886947c4744fa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T15:13:23Z","title_canon_sha256":"6a1b44ba4bfdb13d9de65f8721ca48590f170940adb075df6d2dc291e48a9938"},"schema_version":"1.0","source":{"id":"2506.08883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08883","created_at":"2026-07-05T11:35:14Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08883v2","created_at":"2026-07-05T11:35:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08883","created_at":"2026-07-05T11:35:14Z"},{"alias_kind":"pith_short_12","alias_value":"6UTOODF7RP5C","created_at":"2026-07-05T11:35:14Z"},{"alias_kind":"pith_short_16","alias_value":"6UTOODF7RP5CNGPX","created_at":"2026-07-05T11:35:14Z"},{"alias_kind":"pith_short_8","alias_value":"6UTOODF7","created_at":"2026-07-05T11:35:14Z"}],"graph_snapshots":[{"event_id":"sha256:d7e07a6d74bc38c9a298522325490ab38684bd1cd1cfed81e4860ffd4157be19","target":"graph","created_at":"2026-07-05T11:35:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.08883/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a permutation, there is a well-developed literature studying the number of ways one can factor it into a product of other permutations subject to certain conditions. We initiate the analogous theory for the type A Iwahori-Hecke algebra by generalizing the notion of factorization in terms of the Jucys-Murphy elements. Some of the oldest and most foundational factorization results for the symmetric groups pertain to the long cycle. Our main results give q-deformations of these long cycle factorizations and reveal q-binomial, q-Catalan, and q-Narayana numbers along the way.","authors_text":"Alejandro H. Morales, Franco Saliola, GaYee Park, Jose Bastidas, Mathieu Guay-Paquet, Sarah Brauner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T15:13:23Z","title":"Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08883","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8786b37fcd4667cf41761974b0e2fcecf4ab993582362302e8f3d9f0ca11b83c","target":"record","created_at":"2026-07-05T11:35:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"81edacd4717492adce26b0e237489a0ae3cdce6103db21075b886947c4744fa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T15:13:23Z","title_canon_sha256":"6a1b44ba4bfdb13d9de65f8721ca48590f170940adb075df6d2dc291e48a9938"},"schema_version":"1.0","source":{"id":"2506.08883","kind":"arxiv","version":2}},"canonical_sha256":"f526e70cbf8bfa2699f7ba48cdd03dbf6d63bb6468ed483ca4e748b4c98f3897","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f526e70cbf8bfa2699f7ba48cdd03dbf6d63bb6468ed483ca4e748b4c98f3897","first_computed_at":"2026-07-05T11:35:14.270953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:35:14.270953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GnXOQPDGmR4amhzlZMxAfdz9y5p3kZ5jZcjeApWCo16rjElHT/Y7tKkgBZOSdANddrJyuU/Hz5YwkUWyWr6GAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:35:14.271472Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.08883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8786b37fcd4667cf41761974b0e2fcecf4ab993582362302e8f3d9f0ca11b83c","sha256:d7e07a6d74bc38c9a298522325490ab38684bd1cd1cfed81e4860ffd4157be19"],"state_sha256":"54e9b579712eb57fd487d56163333f2c734a9b391b9e055d4d5a04e78a34e2bd"}