{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:SQ2VP5IXD6RRWU2CQHL3MD3I7R","short_pith_number":"pith:SQ2VP5IX","canonical_record":{"source":{"id":"0909.5418","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-09-29T19:39:59Z","cross_cats_sorted":["hep-th","math.DG"],"title_canon_sha256":"9eea60ea392285b5b624d6425f6709f129ffd5123cb85220b378f12755fc180b","abstract_canon_sha256":"5d1bcd4daea5bf8b5fb62dcf1ba0d9648e7c38a5b7d8a50d64462ae612b027d7"},"schema_version":"1.0"},"canonical_sha256":"943557f5171fa31b534281d7b60f68fc5785d2b65b53836de981ae85639f1b72","source":{"kind":"arxiv","id":"0909.5418","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.5418","created_at":"2026-05-18T03:44:24Z"},{"alias_kind":"arxiv_version","alias_value":"0909.5418v2","created_at":"2026-05-18T03:44:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5418","created_at":"2026-05-18T03:44:24Z"},{"alias_kind":"pith_short_12","alias_value":"SQ2VP5IXD6RR","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SQ2VP5IXD6RRWU2C","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SQ2VP5IX","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:SQ2VP5IXD6RRWU2CQHL3MD3I7R","target":"record","payload":{"canonical_record":{"source":{"id":"0909.5418","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-09-29T19:39:59Z","cross_cats_sorted":["hep-th","math.DG"],"title_canon_sha256":"9eea60ea392285b5b624d6425f6709f129ffd5123cb85220b378f12755fc180b","abstract_canon_sha256":"5d1bcd4daea5bf8b5fb62dcf1ba0d9648e7c38a5b7d8a50d64462ae612b027d7"},"schema_version":"1.0"},"canonical_sha256":"943557f5171fa31b534281d7b60f68fc5785d2b65b53836de981ae85639f1b72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:24.889696Z","signature_b64":"jLFQu2q/9vT6Myw8KHLAbMFm68WOkbDoW+qqTcjs5LOnr7dO7SdUujmRG/+UEtPdydMbYdORCF/RIHg2LjEnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"943557f5171fa31b534281d7b60f68fc5785d2b65b53836de981ae85639f1b72","last_reissued_at":"2026-05-18T03:44:24.888863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:24.888863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.5418","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":"2026-05-18T03:44:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HqKoASJDnrFg4Uja4WeMGhzKEbIzlxaalCUf0WnBr+AlLPdbY1JNrR+aL/7pe8WPzS48JlsjEm1xvUAzmXTYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T15:45:55.764970Z"},"content_sha256":"d900436e235e141935b667574335565d8a5d1a237d2eb7c3d7d0b09f9c218c0f","schema_version":"1.0","event_id":"sha256:d900436e235e141935b667574335565d8a5d1a237d2eb7c3d7d0b09f9c218c0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:SQ2VP5IXD6RRWU2CQHL3MD3I7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomology and Hodge Theory on Symplectic Manifolds: I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.DG"],"primary_cat":"math.SG","authors_text":"Li-Sheng Tseng, Shing-Tung Yau","submitted_at":"2009-09-29T19:39:59Z","abstract_excerpt":"We introduce new finite-dimensional cohomologies on symplectic manifolds. Each exhibits Lefschetz decomposition and contains a unique harmonic representative within each class. Associated with each cohomology is a primitive cohomology defined purely on the space of primitive forms. We identify the dual currents of lagrangians and more generally coisotropic submanifolds with elements of a primitive cohomology, which dualizes to a homology on coisotropic chains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5418","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":"2026-05-18T03:44:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TxbMNeIADlKv0wnSfm7wUUXadjs/sn/OcjrIpdulQc4WwTmP23iNtpdt7zNpb535IyKDTSW2kqtQzhLRIULqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T15:45:55.765461Z"},"content_sha256":"3ec63fcd5927e268bf3ae37ce3b97e9fae6f3879ca733ca7243e48e21b86a178","schema_version":"1.0","event_id":"sha256:3ec63fcd5927e268bf3ae37ce3b97e9fae6f3879ca733ca7243e48e21b86a178"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQ2VP5IXD6RRWU2CQHL3MD3I7R/bundle.json","state_url":"https://pith.science/pith/SQ2VP5IXD6RRWU2CQHL3MD3I7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQ2VP5IXD6RRWU2CQHL3MD3I7R/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":"2026-08-21T15:45:55Z","links":{"resolver":"https://pith.science/pith/SQ2VP5IXD6RRWU2CQHL3MD3I7R","bundle":"https://pith.science/pith/SQ2VP5IXD6RRWU2CQHL3MD3I7R/bundle.json","state":"https://pith.science/pith/SQ2VP5IXD6RRWU2CQHL3MD3I7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQ2VP5IXD6RRWU2CQHL3MD3I7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:SQ2VP5IXD6RRWU2CQHL3MD3I7R","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":"5d1bcd4daea5bf8b5fb62dcf1ba0d9648e7c38a5b7d8a50d64462ae612b027d7","cross_cats_sorted":["hep-th","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-09-29T19:39:59Z","title_canon_sha256":"9eea60ea392285b5b624d6425f6709f129ffd5123cb85220b378f12755fc180b"},"schema_version":"1.0","source":{"id":"0909.5418","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.5418","created_at":"2026-05-18T03:44:24Z"},{"alias_kind":"arxiv_version","alias_value":"0909.5418v2","created_at":"2026-05-18T03:44:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5418","created_at":"2026-05-18T03:44:24Z"},{"alias_kind":"pith_short_12","alias_value":"SQ2VP5IXD6RR","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SQ2VP5IXD6RRWU2C","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SQ2VP5IX","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:3ec63fcd5927e268bf3ae37ce3b97e9fae6f3879ca733ca7243e48e21b86a178","target":"graph","created_at":"2026-05-18T03:44:24Z","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 introduce new finite-dimensional cohomologies on symplectic manifolds. Each exhibits Lefschetz decomposition and contains a unique harmonic representative within each class. Associated with each cohomology is a primitive cohomology defined purely on the space of primitive forms. We identify the dual currents of lagrangians and more generally coisotropic submanifolds with elements of a primitive cohomology, which dualizes to a homology on coisotropic chains.","authors_text":"Li-Sheng Tseng, Shing-Tung Yau","cross_cats":["hep-th","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-09-29T19:39:59Z","title":"Cohomology and Hodge Theory on Symplectic Manifolds: I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5418","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:d900436e235e141935b667574335565d8a5d1a237d2eb7c3d7d0b09f9c218c0f","target":"record","created_at":"2026-05-18T03:44:24Z","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":"5d1bcd4daea5bf8b5fb62dcf1ba0d9648e7c38a5b7d8a50d64462ae612b027d7","cross_cats_sorted":["hep-th","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-09-29T19:39:59Z","title_canon_sha256":"9eea60ea392285b5b624d6425f6709f129ffd5123cb85220b378f12755fc180b"},"schema_version":"1.0","source":{"id":"0909.5418","kind":"arxiv","version":2}},"canonical_sha256":"943557f5171fa31b534281d7b60f68fc5785d2b65b53836de981ae85639f1b72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"943557f5171fa31b534281d7b60f68fc5785d2b65b53836de981ae85639f1b72","first_computed_at":"2026-05-18T03:44:24.888863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:24.888863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jLFQu2q/9vT6Myw8KHLAbMFm68WOkbDoW+qqTcjs5LOnr7dO7SdUujmRG/+UEtPdydMbYdORCF/RIHg2LjEnCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:24.889696Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.5418","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d900436e235e141935b667574335565d8a5d1a237d2eb7c3d7d0b09f9c218c0f","sha256:3ec63fcd5927e268bf3ae37ce3b97e9fae6f3879ca733ca7243e48e21b86a178"],"state_sha256":"fdee577fd0555d303c89d18ffbbd54914372f8bfa01b43ca6b36274638b9f240"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MgBxe1uv32N1jV5Yv78K4iNK5cuNCkl0q0VCKJv+Q9BdPLP+gFZVxAWWU6SGpQsG/x7AHw9WD5otfK85z6uUDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T15:45:55.769817Z","bundle_sha256":"ade96830912a6770216b95671df1fffced376945f1a3a1786bfea315c009edac"}}