{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:GRLRASSVRZWL5C3M4HILESUGLJ","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":"69fcf5e1c0b65368fd3ff1ea0b8a02abe9a13cd5269e3a6837814905c51d9c3a","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.QA","submitted_at":"2006-01-11T22:13:46Z","title_canon_sha256":"6a58ae125549eafedb0e8dbea3b85081a6b18a96127ec48fa4ee064e2bf42d47"},"schema_version":"1.0","source":{"id":"math/0601267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0601267","created_at":"2026-07-05T08:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"math/0601267v1","created_at":"2026-07-05T08:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601267","created_at":"2026-07-05T08:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"GRLRASSVRZWL","created_at":"2026-07-05T08:41:25Z"},{"alias_kind":"pith_short_16","alias_value":"GRLRASSVRZWL5C3M","created_at":"2026-07-05T08:41:25Z"},{"alias_kind":"pith_short_8","alias_value":"GRLRASSV","created_at":"2026-07-05T08:41:25Z"}],"graph_snapshots":[{"event_id":"sha256:071b71cb8003916e9e1a1fc6e462fbf35bc54ed6218aa431c3a7e5d2d4ea4582","target":"graph","created_at":"2026-07-05T08:41:25Z","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/math/0601267/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The colored HOMFLY polynomial is the quantum invariant of oriented links in $S^3$ associated with irreducible representations of the quantum group $U_q(\\mathrm{sl}_N)$. In this paper, using an approach to calculate quantum invariants of links via cabling-projection rule, we derive a formula for the colored HOMFLY polynomial in terms of the characters of the Hecke algebras and Schur polynomials. The technique leads to a fairly simple formula for the colored HOMFLY polynomial of torus links. This formula allows us to test the Labastida-Mari\\~no-Vafa conjecture, which reveals a deep relationship ","authors_text":"Hao Zheng, Xiao-Song Lin","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2006-01-11T22:13:46Z","title":"On the Hecke algebras and the colored HOMFLY polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601267","kind":"arxiv","version":1},"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":"sha256:6e83903441f432a310fd31f9a8a3a6648c5c652e3b3ff04a80e6cbf10e5cf099","target":"record","created_at":"2026-07-05T08:41:25Z","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":"69fcf5e1c0b65368fd3ff1ea0b8a02abe9a13cd5269e3a6837814905c51d9c3a","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.QA","submitted_at":"2006-01-11T22:13:46Z","title_canon_sha256":"6a58ae125549eafedb0e8dbea3b85081a6b18a96127ec48fa4ee064e2bf42d47"},"schema_version":"1.0","source":{"id":"math/0601267","kind":"arxiv","version":1}},"canonical_sha256":"3457104a558e6cbe8b6ce1d0b24a865a41824ba0d6d6b5ab81a18b2409e15288","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3457104a558e6cbe8b6ce1d0b24a865a41824ba0d6d6b5ab81a18b2409e15288","first_computed_at":"2026-07-05T08:41:25.073862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:41:25.073862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/qq79DqBOLz4uJlEaYYDnNUePACn+JO2rF/T2UwW6NWbn83A2emL4MqYElSciD6t3tftBI4UeMIeDCYbms5xAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:41:25.074323Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0601267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e83903441f432a310fd31f9a8a3a6648c5c652e3b3ff04a80e6cbf10e5cf099","sha256:071b71cb8003916e9e1a1fc6e462fbf35bc54ed6218aa431c3a7e5d2d4ea4582"],"state_sha256":"b956725a35cbb7119f02a7e22758563b6a1c8603dac11d397f3c79737bc4b3b3"}