{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:YLWTQGBGOZX627WSR5RLOC4VM4","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":"db6e67cb1334e2b69760e4b912c75f2b942e4542eb6fda0566f5999a4c0053d7","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AG","submitted_at":"2007-10-17T05:13:11Z","title_canon_sha256":"16e9ee7c9b6411530f006b6c327893a0b165dc35c0695128946c4259774f03ef"},"schema_version":"1.0","source":{"id":"0710.3216","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3216","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3216v2","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3216","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"pith_short_12","alias_value":"YLWTQGBGOZX6","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"YLWTQGBGOZX627WS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"YLWTQGBG","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:625b048f52101e818504c6d92eb56e75dd8fb38f14f37eb65df28bf6f25447cd","target":"graph","created_at":"2026-05-18T02:16:10Z","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":"Using derived categories of equivariant coherent sheaves we construct a knot homology theory which categorifies the quantum sl(m) knot polynomial. Our knot homology naturally satisfies the categorified MOY relations and is conjecturally isomorphic to Khovanov-Rozansky homology. Our construction is motivated by the geometric Satake correspondence and is related to Manolescu's by homological mirror symmetry.","authors_text":"Joel Kamnitzer, Sabin Cautis","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2007-10-17T05:13:11Z","title":"Knot homology via derived categories of coherent sheaves II, sl(m) case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3216","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":"sha256:7b60fdf89d8c083c4b6e720518e0a647385bcde3105fb069d0e65c862972ef4e","target":"record","created_at":"2026-05-18T02:16:10Z","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":"db6e67cb1334e2b69760e4b912c75f2b942e4542eb6fda0566f5999a4c0053d7","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AG","submitted_at":"2007-10-17T05:13:11Z","title_canon_sha256":"16e9ee7c9b6411530f006b6c327893a0b165dc35c0695128946c4259774f03ef"},"schema_version":"1.0","source":{"id":"0710.3216","kind":"arxiv","version":2}},"canonical_sha256":"c2ed381826766fed7ed28f62b70b956737ee6ca0f65e09108463d2ebdc10877f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2ed381826766fed7ed28f62b70b956737ee6ca0f65e09108463d2ebdc10877f","first_computed_at":"2026-05-18T02:16:10.341675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:10.341675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tOJmCbL3qoIBzdMRAewex3DFSQysDkzKJOhKKlccqLmeRhSePaIAllFY9p5QvpMXtGnz+jNngEdn08pAoLKOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:10.342357Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.3216","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b60fdf89d8c083c4b6e720518e0a647385bcde3105fb069d0e65c862972ef4e","sha256:625b048f52101e818504c6d92eb56e75dd8fb38f14f37eb65df28bf6f25447cd"],"state_sha256":"b9f96b57530b7bde22a179963ff98714a392c86d186918e2ab41a2da9e8a6742"}