{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:E4K47RN5ONMD5EPFGJK47OSEWT","short_pith_number":"pith:E4K47RN5","canonical_record":{"source":{"id":"math/0103190","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2001-03-27T23:03:51Z","cross_cats_sorted":[],"title_canon_sha256":"2017cd46cd4a8614b28dd8cfbd3fae07672457f08a18ca915fa277855e194264","abstract_canon_sha256":"1e7374ab54d6aae0b5e1dae8968a679c401c0acc56e089d746a381aa755fd8bd"},"schema_version":"1.0"},"canonical_sha256":"2715cfc5bd73583e91e53255cfba44b4cc099f4bcbd1be25e2b6662ecfbe4719","source":{"kind":"arxiv","id":"math/0103190","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0103190","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/0103190v2","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0103190","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"pith_short_12","alias_value":"E4K47RN5ONMD","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"E4K47RN5ONMD5EPF","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"E4K47RN5","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:E4K47RN5ONMD5EPFGJK47OSEWT","target":"record","payload":{"canonical_record":{"source":{"id":"math/0103190","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2001-03-27T23:03:51Z","cross_cats_sorted":[],"title_canon_sha256":"2017cd46cd4a8614b28dd8cfbd3fae07672457f08a18ca915fa277855e194264","abstract_canon_sha256":"1e7374ab54d6aae0b5e1dae8968a679c401c0acc56e089d746a381aa755fd8bd"},"schema_version":"1.0"},"canonical_sha256":"2715cfc5bd73583e91e53255cfba44b4cc099f4bcbd1be25e2b6662ecfbe4719","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:33.324637Z","signature_b64":"hB5TDuzgwOhWDlJZoMKDg/xSzXj4gbGYnpXx9S9ub6vAnbrmAySW5x9xApj9jpWrIfRWlU8dlznHeREehe25Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2715cfc5bd73583e91e53255cfba44b4cc099f4bcbd1be25e2b6662ecfbe4719","last_reissued_at":"2026-05-18T02:41:33.324151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:33.324151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0103190","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nftE/iEmILSlT2/gjcRBQoR0+5i67D1YQYGwr44rM1nOdPxSuzt5Z8MvBluVDQk8rl2lm0qcMe9v6bgrwG3IDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:11:47.418442Z"},"content_sha256":"51fb90de89b8103a04fbadca91ef7e8937706b45c06e1f4dd1e4e3e3b365006d","schema_version":"1.0","event_id":"sha256:51fb90de89b8103a04fbadca91ef7e8937706b45c06e1f4dd1e4e3e3b365006d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:E4K47RN5ONMD5EPFGJK47OSEWT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A functor-valued invariant of tangles","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Mikhail Khovanov","submitted_at":"2001-03-27T23:03:51Z","abstract_excerpt":"We construct a family of rings. To a plane diagram of a tangle we associate a complex of bimodules over these rings. Chain homotopy equivalence class of this complex is an invariant of the tangle. On the level of Grothendieck groups this invariant descends to the Kauffman bracket of the tangle. When the tangle is a link, the invariant specializes to the bigraded cohomology theory introduced in our earlier work."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0103190","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WS9dcql//BC55UJtnwZWTHndBEkxCMcAhvb+u3AhAtABxIyXCJWDynMNFwLvB5/z/pGLxg9Qu5JZ+mtdp55NBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:11:47.418782Z"},"content_sha256":"2e6c7a157c701d1a280ab491fab7d1efa281d2ee92f8f8705693ba2a4e68f3ea","schema_version":"1.0","event_id":"sha256:2e6c7a157c701d1a280ab491fab7d1efa281d2ee92f8f8705693ba2a4e68f3ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E4K47RN5ONMD5EPFGJK47OSEWT/bundle.json","state_url":"https://pith.science/pith/E4K47RN5ONMD5EPFGJK47OSEWT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E4K47RN5ONMD5EPFGJK47OSEWT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T13:11:47Z","links":{"resolver":"https://pith.science/pith/E4K47RN5ONMD5EPFGJK47OSEWT","bundle":"https://pith.science/pith/E4K47RN5ONMD5EPFGJK47OSEWT/bundle.json","state":"https://pith.science/pith/E4K47RN5ONMD5EPFGJK47OSEWT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E4K47RN5ONMD5EPFGJK47OSEWT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:E4K47RN5ONMD5EPFGJK47OSEWT","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":"1e7374ab54d6aae0b5e1dae8968a679c401c0acc56e089d746a381aa755fd8bd","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2001-03-27T23:03:51Z","title_canon_sha256":"2017cd46cd4a8614b28dd8cfbd3fae07672457f08a18ca915fa277855e194264"},"schema_version":"1.0","source":{"id":"math/0103190","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0103190","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/0103190v2","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0103190","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"pith_short_12","alias_value":"E4K47RN5ONMD","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"E4K47RN5ONMD5EPF","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"E4K47RN5","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:2e6c7a157c701d1a280ab491fab7d1efa281d2ee92f8f8705693ba2a4e68f3ea","target":"graph","created_at":"2026-05-18T02:41:33Z","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 construct a family of rings. To a plane diagram of a tangle we associate a complex of bimodules over these rings. Chain homotopy equivalence class of this complex is an invariant of the tangle. On the level of Grothendieck groups this invariant descends to the Kauffman bracket of the tangle. When the tangle is a link, the invariant specializes to the bigraded cohomology theory introduced in our earlier work.","authors_text":"Mikhail Khovanov","cross_cats":[],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2001-03-27T23:03:51Z","title":"A functor-valued invariant of tangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0103190","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":"sha256:51fb90de89b8103a04fbadca91ef7e8937706b45c06e1f4dd1e4e3e3b365006d","target":"record","created_at":"2026-05-18T02:41:33Z","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":"1e7374ab54d6aae0b5e1dae8968a679c401c0acc56e089d746a381aa755fd8bd","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2001-03-27T23:03:51Z","title_canon_sha256":"2017cd46cd4a8614b28dd8cfbd3fae07672457f08a18ca915fa277855e194264"},"schema_version":"1.0","source":{"id":"math/0103190","kind":"arxiv","version":2}},"canonical_sha256":"2715cfc5bd73583e91e53255cfba44b4cc099f4bcbd1be25e2b6662ecfbe4719","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2715cfc5bd73583e91e53255cfba44b4cc099f4bcbd1be25e2b6662ecfbe4719","first_computed_at":"2026-05-18T02:41:33.324151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:33.324151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hB5TDuzgwOhWDlJZoMKDg/xSzXj4gbGYnpXx9S9ub6vAnbrmAySW5x9xApj9jpWrIfRWlU8dlznHeREehe25Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:33.324637Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0103190","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51fb90de89b8103a04fbadca91ef7e8937706b45c06e1f4dd1e4e3e3b365006d","sha256:2e6c7a157c701d1a280ab491fab7d1efa281d2ee92f8f8705693ba2a4e68f3ea"],"state_sha256":"9edd83aa7cb86b0530a33ac5884f4da5b0b2e39147ebc8c082cbc3e382a73e6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6KBf7udShVWNAdb52TZ1/UoUyQsiBW/WhzHyhzWt89Xvd/R6cLESwECcKRcA5VxReubb53CxU+aquLBectjCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:11:47.420758Z","bundle_sha256":"c3d5c8807c1fda82f58fb1211297fd15c44258c70bede2c808fd01d8dd821a5a"}}