{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:U3LM3USQV4D65IFHANMQBCYT6W","short_pith_number":"pith:U3LM3USQ","canonical_record":{"source":{"id":"1504.01230","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-04-06T08:14:10Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"59fe613dcb7f5c024aa9a1680984da164d2a744d8564f64cf69e135edee86d18","abstract_canon_sha256":"9df306703139b1ba7c06a58bf7b559943af941f3450622a484a56a55c05a7d26"},"schema_version":"1.0"},"canonical_sha256":"a6d6cdd250af07eea0a70359008b13f5ad38c9d2dce733e330f6636b84f8c19f","source":{"kind":"arxiv","id":"1504.01230","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01230","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01230v2","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01230","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"pith_short_12","alias_value":"U3LM3USQV4D6","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U3LM3USQV4D65IFH","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U3LM3USQ","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:U3LM3USQV4D65IFHANMQBCYT6W","target":"record","payload":{"canonical_record":{"source":{"id":"1504.01230","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-04-06T08:14:10Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"59fe613dcb7f5c024aa9a1680984da164d2a744d8564f64cf69e135edee86d18","abstract_canon_sha256":"9df306703139b1ba7c06a58bf7b559943af941f3450622a484a56a55c05a7d26"},"schema_version":"1.0"},"canonical_sha256":"a6d6cdd250af07eea0a70359008b13f5ad38c9d2dce733e330f6636b84f8c19f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:38.282249Z","signature_b64":"3iwzaZz1Smd+H4VloKTBjXYUszd6kZvB0cgQGMV92wH7K7Ts+qsW8xXM7uV2tkftBSNkI2lA9zfdXs3VJqXeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6d6cdd250af07eea0a70359008b13f5ad38c9d2dce733e330f6636b84f8c19f","last_reissued_at":"2026-05-18T00:15:38.281574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:38.281574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.01230","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":"2026-05-18T00:15:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vARWQdpfQxaTva6g+PC70hxeUJQWFkYRMQGSoXaZlrGo6uVZMq5+gaEnD9b0+5iYPZP35SZdStguKAB07nfZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:22:04.988947Z"},"content_sha256":"8254827bceec1c442766a622fdcebc058d68d1fb31e1e6fe4c726e9f1110e049","schema_version":"1.0","event_id":"sha256:8254827bceec1c442766a622fdcebc058d68d1fb31e1e6fe4c726e9f1110e049"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:U3LM3USQV4D65IFHANMQBCYT6W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Khovanov homology from Floer cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Ivan Smith, Mohammed Abouzaid","submitted_at":"2015-04-06T08:14:10Z","abstract_excerpt":"This paper realises the Khovanov homology of a link in the 3-sphere as a Lagrangian Floer cohomology group, establishing a conjecture of Seidel and the second author. The starting point is the previously established formality theorem for the symplectic arc algebra over a field k of characteristic zero. Here we prove the symplectic cup and cap bimodules which relate different symplectic arc algebras are themselves formal over k, and construct a long exact triangle for symplectic Khovanov cohomology. We then prove the symplectic and combinatorial arc algebras are isomorphic over the integers in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01230","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":"2026-05-18T00:15:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aueV8a84ikJ0FpKGVF0N3nBvl+djFdb/7tpkBIixTvC9RkfRg70/d3LF3oMOQh9UxbQezV+RebHssugqhl3+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:22:04.989296Z"},"content_sha256":"3aa837bc6d9a5aef0fa6a4aeec8f56c9be49a28422fb57a151bd24587a17c80c","schema_version":"1.0","event_id":"sha256:3aa837bc6d9a5aef0fa6a4aeec8f56c9be49a28422fb57a151bd24587a17c80c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U3LM3USQV4D65IFHANMQBCYT6W/bundle.json","state_url":"https://pith.science/pith/U3LM3USQV4D65IFHANMQBCYT6W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U3LM3USQV4D65IFHANMQBCYT6W/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":"2026-06-05T10:22:04Z","links":{"resolver":"https://pith.science/pith/U3LM3USQV4D65IFHANMQBCYT6W","bundle":"https://pith.science/pith/U3LM3USQV4D65IFHANMQBCYT6W/bundle.json","state":"https://pith.science/pith/U3LM3USQV4D65IFHANMQBCYT6W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U3LM3USQV4D65IFHANMQBCYT6W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:U3LM3USQV4D65IFHANMQBCYT6W","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":"9df306703139b1ba7c06a58bf7b559943af941f3450622a484a56a55c05a7d26","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-04-06T08:14:10Z","title_canon_sha256":"59fe613dcb7f5c024aa9a1680984da164d2a744d8564f64cf69e135edee86d18"},"schema_version":"1.0","source":{"id":"1504.01230","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01230","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01230v2","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01230","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"pith_short_12","alias_value":"U3LM3USQV4D6","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U3LM3USQV4D65IFH","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U3LM3USQ","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:3aa837bc6d9a5aef0fa6a4aeec8f56c9be49a28422fb57a151bd24587a17c80c","target":"graph","created_at":"2026-05-18T00:15:38Z","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":"This paper realises the Khovanov homology of a link in the 3-sphere as a Lagrangian Floer cohomology group, establishing a conjecture of Seidel and the second author. The starting point is the previously established formality theorem for the symplectic arc algebra over a field k of characteristic zero. Here we prove the symplectic cup and cap bimodules which relate different symplectic arc algebras are themselves formal over k, and construct a long exact triangle for symplectic Khovanov cohomology. We then prove the symplectic and combinatorial arc algebras are isomorphic over the integers in ","authors_text":"Ivan Smith, Mohammed Abouzaid","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-04-06T08:14:10Z","title":"Khovanov homology from Floer cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01230","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":"sha256:8254827bceec1c442766a622fdcebc058d68d1fb31e1e6fe4c726e9f1110e049","target":"record","created_at":"2026-05-18T00:15:38Z","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":"9df306703139b1ba7c06a58bf7b559943af941f3450622a484a56a55c05a7d26","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-04-06T08:14:10Z","title_canon_sha256":"59fe613dcb7f5c024aa9a1680984da164d2a744d8564f64cf69e135edee86d18"},"schema_version":"1.0","source":{"id":"1504.01230","kind":"arxiv","version":2}},"canonical_sha256":"a6d6cdd250af07eea0a70359008b13f5ad38c9d2dce733e330f6636b84f8c19f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6d6cdd250af07eea0a70359008b13f5ad38c9d2dce733e330f6636b84f8c19f","first_computed_at":"2026-05-18T00:15:38.281574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:38.281574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3iwzaZz1Smd+H4VloKTBjXYUszd6kZvB0cgQGMV92wH7K7Ts+qsW8xXM7uV2tkftBSNkI2lA9zfdXs3VJqXeCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:38.282249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01230","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8254827bceec1c442766a622fdcebc058d68d1fb31e1e6fe4c726e9f1110e049","sha256:3aa837bc6d9a5aef0fa6a4aeec8f56c9be49a28422fb57a151bd24587a17c80c"],"state_sha256":"dc1c8a7fce1308b8b7b7f91242e7445c8b4b4e748bf5895571a1e81530355993"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GUNP0xqFuMmeg+5wFLG40zPv1Wsgo99taW1rr/Mq3mXEgWhv9gcw3bcM0Bakqhg1zG3ESShGy37vAnuBBIkjBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:22:04.991379Z","bundle_sha256":"4801239ccea8a277b66ab92ccecc310a43ea6177d66679555c7bb8f5e82c34cb"}}