{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YYUKBGWTTSIPVLTFWGFX7BJ7FG","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":"759ec926b2f3a7d337b5f7af7e9d48d2ad96ed41d2838f16f4368f9ce2716b0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-11-10T16:10:32Z","title_canon_sha256":"00d1ad0079d429253bee631f24c5752e5ffd7a37f8ea1f40a29636bb507c694b"},"schema_version":"1.0","source":{"id":"1211.2334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2334","created_at":"2026-05-18T03:41:03Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2334v1","created_at":"2026-05-18T03:41:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2334","created_at":"2026-05-18T03:41:03Z"},{"alias_kind":"pith_short_12","alias_value":"YYUKBGWTTSIP","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YYUKBGWTTSIPVLTF","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YYUKBGWT","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:00966e813a14f7b89701e729bc06bcc5edf45d6fd29e51c80cb8144aa2b8799a","target":"graph","created_at":"2026-05-18T03:41:03Z","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":"T.-J. Li and W. Zhang defined an almost complex structure $J$ on a manifold $X$ to be {\\em \\Cpf}, if the second de Rham cohomology group can be decomposed as a direct sum of the subgroups whose elements are cohomology classes admitting $J$-invariant and $J$-anti-invariant representatives. It turns out (see T. Draghici, T.-J. Li and W. Zhang) that any almost complex structure on a 4-dimensional compact manifold is \\Cpf. We study the $J$-invariant and $J$-anti-invariant cohomology subgroups on almost complex manifolds, possibly non compact. In particular, we prove an analytic continuation result","authors_text":"Adriano Tomassini, Costantino Medori, Richard Hind","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-11-10T16:10:32Z","title":"On non-pure forms on almost complex manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2334","kind":"arxiv","version":1},"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":"sha256:32bfe12ccca9fc9dfcbdca232aaf33bdbb37cc7a4b4eebfa85543f8d023588da","target":"record","created_at":"2026-05-18T03:41:03Z","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":"759ec926b2f3a7d337b5f7af7e9d48d2ad96ed41d2838f16f4368f9ce2716b0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-11-10T16:10:32Z","title_canon_sha256":"00d1ad0079d429253bee631f24c5752e5ffd7a37f8ea1f40a29636bb507c694b"},"schema_version":"1.0","source":{"id":"1211.2334","kind":"arxiv","version":1}},"canonical_sha256":"c628a09ad39c90faae65b18b7f853f29ba5c00aea244ebdf80ba542b0e16a278","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c628a09ad39c90faae65b18b7f853f29ba5c00aea244ebdf80ba542b0e16a278","first_computed_at":"2026-05-18T03:41:03.715865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:03.715865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"noX1a7K3yL+92pir1Tq/ERcXqbwWrj18zz2KbqR08MZ0ru956LBFjgg76/mjg50nY1EKzUQYlHu7d+k5GQ4LDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:03.716563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32bfe12ccca9fc9dfcbdca232aaf33bdbb37cc7a4b4eebfa85543f8d023588da","sha256:00966e813a14f7b89701e729bc06bcc5edf45d6fd29e51c80cb8144aa2b8799a"],"state_sha256":"24366b48ff4861a4dd1a3b4ab5a9a8a7317294e0a7e133981d92ef74dd2e30e3"}