{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6LORANNQ4PY6KPWQWKXONPDJEC","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":"580091eb919f81b75ad6225dff40461b0f5d51209a525a715ff1ea4b7c3b65f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-02-02T23:21:48Z","title_canon_sha256":"ce3c85dd806e3b294ade3ed376e33b6af3528b7eb019db38dbf2ddbda81fde1b"},"schema_version":"1.0","source":{"id":"1102.0586","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0586","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0586v1","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0586","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"pith_short_12","alias_value":"6LORANNQ4PY6","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6LORANNQ4PY6KPWQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6LORANNQ","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:6e832728894596986cdb8306d095890b52b8881dcbdfe2579b328a0361d7b4cd","target":"graph","created_at":"2026-05-18T04:30:04Z","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"},"paper":{"abstract_excerpt":"We generalize the Morton-Franks-Williams inequality to the colored $\\mathfrak{sl}(N)$ link homology defined in arXiv:0907.0695, which gives infinitely many new bounds for the braid index and the self linking number. A key ingredient of our proof is a composition product for the general MOY graph polynomial, which generalizes that of Wagner arXiv:math/0702230v1.","authors_text":"Hao Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-02-02T23:21:48Z","title":"Colored Morton-Franks-Williams inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0586","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":"sha256:39d59b509452bb1e0c997edd8e8e62cb1b68661d6f0f851d6fba79957c946442","target":"record","created_at":"2026-05-18T04:30:04Z","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":"580091eb919f81b75ad6225dff40461b0f5d51209a525a715ff1ea4b7c3b65f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-02-02T23:21:48Z","title_canon_sha256":"ce3c85dd806e3b294ade3ed376e33b6af3528b7eb019db38dbf2ddbda81fde1b"},"schema_version":"1.0","source":{"id":"1102.0586","kind":"arxiv","version":1}},"canonical_sha256":"f2dd1035b0e3f1e53ed0b2aee6bc692081e4ee8567121ed7129186c36834feea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2dd1035b0e3f1e53ed0b2aee6bc692081e4ee8567121ed7129186c36834feea","first_computed_at":"2026-05-18T04:30:04.402498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:04.402498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"feKQrGQw+Vn3UbCJFpKjkC9tVe4EMfaQCCfgpaBgys7gjgUv2rsJGA6h5Ge3CxD6mzeTDHdekfqQaHBYsOsODA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:04.403131Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0586","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39d59b509452bb1e0c997edd8e8e62cb1b68661d6f0f851d6fba79957c946442","sha256:6e832728894596986cdb8306d095890b52b8881dcbdfe2579b328a0361d7b4cd"],"state_sha256":"4ddb2f49611a72b8b603eba95988e3d51339c065c58c59536fd1658007262329"}