{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:XKBKGP6SC2NPBYIMTRRPGDFQ6X","short_pith_number":"pith:XKBKGP6S","schema_version":"1.0","canonical_sha256":"ba82a33fd2169af0e10c9c62f30cb0f5daa2289142373641236a9a5137ebbf8b","source":{"kind":"arxiv","id":"1402.0427","version":2},"attestation_state":"computed","paper":{"title":"Cohomology and Hodge Theory on Symplectic Manifolds: III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.DG","math.GT"],"primary_cat":"math.SG","authors_text":"Chung-Jun Tsai, Li-Sheng Tseng, Shing-Tung Yau","submitted_at":"2014-02-03T16:53:00Z","abstract_excerpt":"We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Paper I and II as a subset. The filtered cohomologies are finite-dimensional and can be associated with differential elliptic complexes. Algebraically, we show that the filtered cohomologies give a two-sided resolution of Lefschetz maps, and thereby, they are directly related to the kernels and cokernels of the Lefschetz maps. We also introduce a novel, non-associative product operation on differential forms for symplectic manifolds. This product generates"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.0427","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-02-03T16:53:00Z","cross_cats_sorted":["hep-th","math.DG","math.GT"],"title_canon_sha256":"ec8517c22cdfd7d292c451635af847c8fb85608caf898b07fa19d24475277ee5","abstract_canon_sha256":"f6a69e41a80d239ddba935afd9d17a8ff034a5a6d881a82e9a0a4d8cb79a1658"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:41.557361Z","signature_b64":"ZAmEJLo3sp/kCVMafwCZ9LztSkFMFqOprIsgaawoaw4R+jbmw8baa6X9t7peMVOpI5IKleWN1SoqtUEidKggCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba82a33fd2169af0e10c9c62f30cb0f5daa2289142373641236a9a5137ebbf8b","last_reissued_at":"2026-05-18T02:52:41.556753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:41.556753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohomology and Hodge Theory on Symplectic Manifolds: III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.DG","math.GT"],"primary_cat":"math.SG","authors_text":"Chung-Jun Tsai, Li-Sheng Tseng, Shing-Tung Yau","submitted_at":"2014-02-03T16:53:00Z","abstract_excerpt":"We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Paper I and II as a subset. The filtered cohomologies are finite-dimensional and can be associated with differential elliptic complexes. Algebraically, we show that the filtered cohomologies give a two-sided resolution of Lefschetz maps, and thereby, they are directly related to the kernels and cokernels of the Lefschetz maps. We also introduce a novel, non-associative product operation on differential forms for symplectic manifolds. This product generates"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0427","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.0427","created_at":"2026-05-18T02:52:41.556822+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.0427v2","created_at":"2026-05-18T02:52:41.556822+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0427","created_at":"2026-05-18T02:52:41.556822+00:00"},{"alias_kind":"pith_short_12","alias_value":"XKBKGP6SC2NP","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"XKBKGP6SC2NPBYIM","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"XKBKGP6S","created_at":"2026-05-18T12:28:57.508820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XKBKGP6SC2NPBYIMTRRPGDFQ6X","json":"https://pith.science/pith/XKBKGP6SC2NPBYIMTRRPGDFQ6X.json","graph_json":"https://pith.science/api/pith-number/XKBKGP6SC2NPBYIMTRRPGDFQ6X/graph.json","events_json":"https://pith.science/api/pith-number/XKBKGP6SC2NPBYIMTRRPGDFQ6X/events.json","paper":"https://pith.science/paper/XKBKGP6S"},"agent_actions":{"view_html":"https://pith.science/pith/XKBKGP6SC2NPBYIMTRRPGDFQ6X","download_json":"https://pith.science/pith/XKBKGP6SC2NPBYIMTRRPGDFQ6X.json","view_paper":"https://pith.science/paper/XKBKGP6S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.0427&json=true","fetch_graph":"https://pith.science/api/pith-number/XKBKGP6SC2NPBYIMTRRPGDFQ6X/graph.json","fetch_events":"https://pith.science/api/pith-number/XKBKGP6SC2NPBYIMTRRPGDFQ6X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XKBKGP6SC2NPBYIMTRRPGDFQ6X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XKBKGP6SC2NPBYIMTRRPGDFQ6X/action/storage_attestation","attest_author":"https://pith.science/pith/XKBKGP6SC2NPBYIMTRRPGDFQ6X/action/author_attestation","sign_citation":"https://pith.science/pith/XKBKGP6SC2NPBYIMTRRPGDFQ6X/action/citation_signature","submit_replication":"https://pith.science/pith/XKBKGP6SC2NPBYIMTRRPGDFQ6X/action/replication_record"}},"created_at":"2026-05-18T02:52:41.556822+00:00","updated_at":"2026-05-18T02:52:41.556822+00:00"}