{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:YXAYIGKTSDCXAYNJDD2NTCI6JH","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":"13628c1488d7a22e3ba430dcbcc996b2d8fa0bcb3c6ae0487951de08e42817df","cross_cats_sorted":["math.AG","math.AT"],"license":"","primary_cat":"math.DG","submitted_at":"2005-02-25T15:35:59Z","title_canon_sha256":"dc85564addf8b60b4399e85c5ace8cbab35561c38552c468fd5cf0e8f1baaeec"},"schema_version":"1.0","source":{"id":"math/0502540","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502540","created_at":"2026-05-18T04:27:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502540v8","created_at":"2026-05-18T04:27:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502540","created_at":"2026-05-18T04:27:36Z"},{"alias_kind":"pith_short_12","alias_value":"YXAYIGKTSDCX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"YXAYIGKTSDCXAYNJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"YXAYIGKT","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f298af99f75c28ebf7baf2baf67e603510c6e12d604d17406b785f222f86a626","target":"graph","created_at":"2026-05-18T04:27:36Z","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":"Let M be a compact Riemannian manifold equipped with a parallel differential form \\omega. We prove a version of Kaehler identities in this setting. This is used to show that the de Rham algebra of M is weakly equivalent to its subquotient $(H^*_c(M), d)$, called {\\bf the pseudocohomology} of M. When M is compact and Kaehler and \\omega is its Kaehler form, $(H^*_c(M), d)$ is isomorphic to the cohomology algebra of M. This gives another proof of homotopy formality for Kaehler manifolds, originally shown by Deligne, Griffiths, Morgan and Sullivan. We compute $H^i_c(M)$ for a compact G_2-manifold,","authors_text":"Misha Verbitsky","cross_cats":["math.AG","math.AT"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2005-02-25T15:35:59Z","title":"Manifolds with parallel differential forms and Kaehler identities for G_2-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502540","kind":"arxiv","version":8},"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:aa637c6f03a76fb5a74d9eb736239e05f630440cf841d4964122959df7ff2e41","target":"record","created_at":"2026-05-18T04:27:36Z","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":"13628c1488d7a22e3ba430dcbcc996b2d8fa0bcb3c6ae0487951de08e42817df","cross_cats_sorted":["math.AG","math.AT"],"license":"","primary_cat":"math.DG","submitted_at":"2005-02-25T15:35:59Z","title_canon_sha256":"dc85564addf8b60b4399e85c5ace8cbab35561c38552c468fd5cf0e8f1baaeec"},"schema_version":"1.0","source":{"id":"math/0502540","kind":"arxiv","version":8}},"canonical_sha256":"c5c184195390c57061a918f4d9891e49ef28523553fdfb74669929e19e1a5e98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5c184195390c57061a918f4d9891e49ef28523553fdfb74669929e19e1a5e98","first_computed_at":"2026-05-18T04:27:36.592354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:36.592354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GGJPsMa4q34Gzv7BAakktYZpbI9Pphc9OT3skogRFnSkm3KXgLSY7tcJj4vggevKDNeDywGGnopD/gNSEGZyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:36.593092Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0502540","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa637c6f03a76fb5a74d9eb736239e05f630440cf841d4964122959df7ff2e41","sha256:f298af99f75c28ebf7baf2baf67e603510c6e12d604d17406b785f222f86a626"],"state_sha256":"08641fac3f37c2a050e3ef5fa4d43e7da41dbc5a15303b927f9d57ee5dc4b639"}