{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VOZ645UTEHSI7HWNZG73JXIG6Y","short_pith_number":"pith:VOZ645UT","canonical_record":{"source":{"id":"1109.1542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-07T19:37:08Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"69609b25628a943d74a5428183edefc7444a33893cb8d978ccfc7c5cd546aec2","abstract_canon_sha256":"d04c5ac27aef4c14163e6731bf96b961a605d38cda2a2a88909e0a812fa3eb5a"},"schema_version":"1.0"},"canonical_sha256":"abb3ee769321e48f9ecdc9bfb4dd06f63fc525df796bf41e3d64d68e71574a9d","source":{"kind":"arxiv","id":"1109.1542","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1542","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1542v2","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1542","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"VOZ645UTEHSI","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VOZ645UTEHSI7HWN","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VOZ645UT","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VOZ645UTEHSI7HWNZG73JXIG6Y","target":"record","payload":{"canonical_record":{"source":{"id":"1109.1542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-07T19:37:08Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"69609b25628a943d74a5428183edefc7444a33893cb8d978ccfc7c5cd546aec2","abstract_canon_sha256":"d04c5ac27aef4c14163e6731bf96b961a605d38cda2a2a88909e0a812fa3eb5a"},"schema_version":"1.0"},"canonical_sha256":"abb3ee769321e48f9ecdc9bfb4dd06f63fc525df796bf41e3d64d68e71574a9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:18.060184Z","signature_b64":"bVmalWV3UfoKEe0oo6e8FnIesmgRrwy6DtkKgCItYLQUQmFzjJgLRy9amm0kSRMMWcUfTUgz10E5pwY7ccsBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abb3ee769321e48f9ecdc9bfb4dd06f63fc525df796bf41e3d64d68e71574a9d","last_reissued_at":"2026-05-18T02:38:18.059714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:18.059714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.1542","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":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8DVaUBM6tTs3If43XtXY232tfpnNJ0ciH1jjC44CWxgb3ZNhw7AUhjEJWEHyM3duT42vn4p5Fo9amtgcJVGvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:51:30.313532Z"},"content_sha256":"88e92b575a2990931841e16b5807ec24cdfd608658878cc89a7e3325ea7585f2","schema_version":"1.0","event_id":"sha256:88e92b575a2990931841e16b5807ec24cdfd608658878cc89a7e3325ea7585f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VOZ645UTEHSI7HWNZG73JXIG6Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Knot contact homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"John Etnyre, Lenhard Ng, Michael Sullivan, Tobias Ekholm","submitted_at":"2011-09-07T19:37:08Z","abstract_excerpt":"The conormal lift of a link $K$ in $\\R^3$ is a Legendrian submanifold $\\Lambda_K$ in the unit cotangent bundle $U^* \\R^3$ of $\\R^3$ with contact structure equal to the kernel of the Liouville form. Knot contact homology, a topological link invariant of $K$, is defined as the Legendrian homology of $\\Lambda_K$, the homology of a differential graded algebra generated by Reeb chords whose differential counts holomorphic disks in the symplectization $\\R \\times U^*\\R^3$ with Lagrangian boundary condition $\\R \\times \\Lambda_K$.\n  We perform an explicit and complete computation of the Legendrian homo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1542","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":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5GmbSJSVr9WcbH1G194mg+kiiKbwSkTI9GkCViV2+yMc3SgTrL933i+mcGnyjgTJQWOd+lIV1pxJl5jn6w0nBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:51:30.314177Z"},"content_sha256":"2e331620167b5151a87ecdb2372bc5fab68453dc2fa8694c426f682ce1f96af8","schema_version":"1.0","event_id":"sha256:2e331620167b5151a87ecdb2372bc5fab68453dc2fa8694c426f682ce1f96af8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VOZ645UTEHSI7HWNZG73JXIG6Y/bundle.json","state_url":"https://pith.science/pith/VOZ645UTEHSI7HWNZG73JXIG6Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VOZ645UTEHSI7HWNZG73JXIG6Y/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":"2026-05-22T11:51:30Z","links":{"resolver":"https://pith.science/pith/VOZ645UTEHSI7HWNZG73JXIG6Y","bundle":"https://pith.science/pith/VOZ645UTEHSI7HWNZG73JXIG6Y/bundle.json","state":"https://pith.science/pith/VOZ645UTEHSI7HWNZG73JXIG6Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VOZ645UTEHSI7HWNZG73JXIG6Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VOZ645UTEHSI7HWNZG73JXIG6Y","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":"d04c5ac27aef4c14163e6731bf96b961a605d38cda2a2a88909e0a812fa3eb5a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-07T19:37:08Z","title_canon_sha256":"69609b25628a943d74a5428183edefc7444a33893cb8d978ccfc7c5cd546aec2"},"schema_version":"1.0","source":{"id":"1109.1542","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1542","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1542v2","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1542","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"VOZ645UTEHSI","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VOZ645UTEHSI7HWN","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VOZ645UT","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:2e331620167b5151a87ecdb2372bc5fab68453dc2fa8694c426f682ce1f96af8","target":"graph","created_at":"2026-05-18T02:38:18Z","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":"The conormal lift of a link $K$ in $\\R^3$ is a Legendrian submanifold $\\Lambda_K$ in the unit cotangent bundle $U^* \\R^3$ of $\\R^3$ with contact structure equal to the kernel of the Liouville form. Knot contact homology, a topological link invariant of $K$, is defined as the Legendrian homology of $\\Lambda_K$, the homology of a differential graded algebra generated by Reeb chords whose differential counts holomorphic disks in the symplectization $\\R \\times U^*\\R^3$ with Lagrangian boundary condition $\\R \\times \\Lambda_K$.\n  We perform an explicit and complete computation of the Legendrian homo","authors_text":"John Etnyre, Lenhard Ng, Michael Sullivan, Tobias Ekholm","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-07T19:37:08Z","title":"Knot contact homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1542","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":"sha256:88e92b575a2990931841e16b5807ec24cdfd608658878cc89a7e3325ea7585f2","target":"record","created_at":"2026-05-18T02:38:18Z","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":"d04c5ac27aef4c14163e6731bf96b961a605d38cda2a2a88909e0a812fa3eb5a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-07T19:37:08Z","title_canon_sha256":"69609b25628a943d74a5428183edefc7444a33893cb8d978ccfc7c5cd546aec2"},"schema_version":"1.0","source":{"id":"1109.1542","kind":"arxiv","version":2}},"canonical_sha256":"abb3ee769321e48f9ecdc9bfb4dd06f63fc525df796bf41e3d64d68e71574a9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abb3ee769321e48f9ecdc9bfb4dd06f63fc525df796bf41e3d64d68e71574a9d","first_computed_at":"2026-05-18T02:38:18.059714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:18.059714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bVmalWV3UfoKEe0oo6e8FnIesmgRrwy6DtkKgCItYLQUQmFzjJgLRy9amm0kSRMMWcUfTUgz10E5pwY7ccsBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:18.060184Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1542","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88e92b575a2990931841e16b5807ec24cdfd608658878cc89a7e3325ea7585f2","sha256:2e331620167b5151a87ecdb2372bc5fab68453dc2fa8694c426f682ce1f96af8"],"state_sha256":"ed10ea10b645d67f8bd1f748161ce76b1f86f6fbf5066571d45d72aa45cbe911"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WgVAo/Tt+uLXobDx3c5v5sHSFoflGu7nDsPETFWr3D56puVgsheG8Gzdpctl44qmcHRzqbDTSUGWBNk+LFBOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T11:51:30.317864Z","bundle_sha256":"91cca9ead8f71bc78ef7ef7119035a67ed242071ffe4b735ca7561dbe9436855"}}