{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:SWBTAX5GA7RAMJOWWUXJZZQZZ5","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":"77409c8c9f1deac8a101209663be2f5dddfd1bf93c5aca69d0e371965d4d3247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2006-06-05T02:23:28Z","title_canon_sha256":"46393a34a3b47fbc68332da2b0a86a67de19339a9e63db03daf3e8efd64dc837"},"schema_version":"1.0","source":{"id":"math/0606095","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606095","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606095v2","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606095","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"SWBTAX5GA7RA","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"SWBTAX5GA7RAMJOW","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"SWBTAX5G","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:b0e5a5d574eb37afd874df38d26458ba4806ccd589f9656e4906f79842d33583","target":"graph","created_at":"2026-05-18T02:57:45Z","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 investigate harmonic forms of geometrically formal metrics, which are defined as those having the exterior product of any two harmonic forms still harmonic. We prove that a formal Sasakian metric can exist only on a real cohomology sphere and that holomorphic forms of a formal K\\\"ahler metric are parallel w.r.t. the Levi-Civita connection. In the general Riemannian case a formal metric with maximal second Betti number is shown to be flat. Finally we prove that a six-dimensional manifold with $b_1 \\neq 1, b_2 \\geqslant 2$ and not having the cohomology algebra of $\\mathbb{T}^3 \\times S^3$ car","authors_text":"Jean-Francois Grosjean, Paul-Andi Nagy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2006-06-05T02:23:28Z","title":"On the cohomology algebra of some classes of geometrically formal manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606095","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:aa6ad67804fdc9b1c838a6b04900fdc4da335c7ea70938fd3c085ef04fdf85fa","target":"record","created_at":"2026-05-18T02:57:45Z","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":"77409c8c9f1deac8a101209663be2f5dddfd1bf93c5aca69d0e371965d4d3247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2006-06-05T02:23:28Z","title_canon_sha256":"46393a34a3b47fbc68332da2b0a86a67de19339a9e63db03daf3e8efd64dc837"},"schema_version":"1.0","source":{"id":"math/0606095","kind":"arxiv","version":2}},"canonical_sha256":"9583305fa607e20625d6b52e9ce619cf7a6f328d35bec30c2902ac16283bdccf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9583305fa607e20625d6b52e9ce619cf7a6f328d35bec30c2902ac16283bdccf","first_computed_at":"2026-05-18T02:57:45.582129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:45.582129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YLUvOMgCaD+CdwnMS0dGugTVFlA0cEnZSv9jZsWXLzpcxQxkGFbcxrmDlUIWp6gtR2sMl3lzps/4xeeyGbc9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:45.582539Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606095","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa6ad67804fdc9b1c838a6b04900fdc4da335c7ea70938fd3c085ef04fdf85fa","sha256:b0e5a5d574eb37afd874df38d26458ba4806ccd589f9656e4906f79842d33583"],"state_sha256":"443729273b8e66378f5a3e12c14bd9b9086bd7e506aac0ac7439341a4ff38acc"}