{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NW5UQURYLCQNJD4LHRO43JS4MY","short_pith_number":"pith:NW5UQURY","canonical_record":{"source":{"id":"1111.7287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-11-30T19:46:05Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"5c2f73d01898b2af0e23b91b5618776bc5fb45b64b32ebf2e2ed7588f9c79a78","abstract_canon_sha256":"fb257d580e15eb645489a60f4c75c548668dcd0aaa4f2fd91934651fdbe3d022"},"schema_version":"1.0"},"canonical_sha256":"6dbb48523858a0d48f8b3c5dcda65c663016bc24cd887fdd5be69c8de1125b57","source":{"kind":"arxiv","id":"1111.7287","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7287","created_at":"2026-05-18T04:07:18Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7287v1","created_at":"2026-05-18T04:07:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7287","created_at":"2026-05-18T04:07:18Z"},{"alias_kind":"pith_short_12","alias_value":"NW5UQURYLCQN","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NW5UQURYLCQNJD4L","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NW5UQURY","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NW5UQURYLCQNJD4LHRO43JS4MY","target":"record","payload":{"canonical_record":{"source":{"id":"1111.7287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-11-30T19:46:05Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"5c2f73d01898b2af0e23b91b5618776bc5fb45b64b32ebf2e2ed7588f9c79a78","abstract_canon_sha256":"fb257d580e15eb645489a60f4c75c548668dcd0aaa4f2fd91934651fdbe3d022"},"schema_version":"1.0"},"canonical_sha256":"6dbb48523858a0d48f8b3c5dcda65c663016bc24cd887fdd5be69c8de1125b57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:18.213767Z","signature_b64":"oWWczp9eLe2ZkwxaFhREHV4TJg9WbHvvpsUALCNqxvARyUS/qSuvBeLg+52+2SAv+LTT6IyRlKr5Ac3X5FrMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dbb48523858a0d48f8b3c5dcda65c663016bc24cd887fdd5be69c8de1125b57","last_reissued_at":"2026-05-18T04:07:18.212916Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:18.212916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.7287","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QGkpMlli3OWyS/kEzli4X2copWhUwyz3wtz9P3KEoZ3HBU/gPZTACBZLs48UjhPFMWlBJmnCCu4vy0Xtsi9PDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:06:35.305225Z"},"content_sha256":"aafefb191e0355c406de09873ed7c0e7bd2b52ea90a18415a05cbfbb3c32a875","schema_version":"1.0","event_id":"sha256:aafefb191e0355c406de09873ed7c0e7bd2b52ea90a18415a05cbfbb3c32a875"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NW5UQURYLCQNJD4LHRO43JS4MY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on exact forms on almost complex manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Tedi Draghici, Weiyi Zhang","submitted_at":"2011-11-30T19:46:05Z","abstract_excerpt":"Reformulations of Donaldson's \"tamed to compatible\" question are obtained in terms of spaces of exact forms on a compact almost complex manifold $(M^{2n},J)$. In dimension 4, we show that $J$ admits a compatible symplectic form if and only if $J$ admits tamed symplectic forms with arbitrarily given $J$-anti-invariant parts. Some observations about the cohomology of $J$-modified de Rham complexes are also made."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7287","kind":"arxiv","version":1},"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":"2026-05-18T04:07:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YfBSTMPi66bXyF00e791hjwTDlux9cnX6zzuWd2D7FseQFw87BeNSytnj8xvhgSmIOa9FfX368TI3I6WrvduAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:06:35.305703Z"},"content_sha256":"b3917664e1f39ed565aed2a2711739563736ee351d28bf796f25b9dd24aacba5","schema_version":"1.0","event_id":"sha256:b3917664e1f39ed565aed2a2711739563736ee351d28bf796f25b9dd24aacba5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NW5UQURYLCQNJD4LHRO43JS4MY/bundle.json","state_url":"https://pith.science/pith/NW5UQURYLCQNJD4LHRO43JS4MY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NW5UQURYLCQNJD4LHRO43JS4MY/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":"2026-05-26T19:06:35Z","links":{"resolver":"https://pith.science/pith/NW5UQURYLCQNJD4LHRO43JS4MY","bundle":"https://pith.science/pith/NW5UQURYLCQNJD4LHRO43JS4MY/bundle.json","state":"https://pith.science/pith/NW5UQURYLCQNJD4LHRO43JS4MY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NW5UQURYLCQNJD4LHRO43JS4MY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NW5UQURYLCQNJD4LHRO43JS4MY","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":"fb257d580e15eb645489a60f4c75c548668dcd0aaa4f2fd91934651fdbe3d022","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-11-30T19:46:05Z","title_canon_sha256":"5c2f73d01898b2af0e23b91b5618776bc5fb45b64b32ebf2e2ed7588f9c79a78"},"schema_version":"1.0","source":{"id":"1111.7287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7287","created_at":"2026-05-18T04:07:18Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7287v1","created_at":"2026-05-18T04:07:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7287","created_at":"2026-05-18T04:07:18Z"},{"alias_kind":"pith_short_12","alias_value":"NW5UQURYLCQN","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NW5UQURYLCQNJD4L","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NW5UQURY","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:b3917664e1f39ed565aed2a2711739563736ee351d28bf796f25b9dd24aacba5","target":"graph","created_at":"2026-05-18T04:07:18Z","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":"Reformulations of Donaldson's \"tamed to compatible\" question are obtained in terms of spaces of exact forms on a compact almost complex manifold $(M^{2n},J)$. In dimension 4, we show that $J$ admits a compatible symplectic form if and only if $J$ admits tamed symplectic forms with arbitrarily given $J$-anti-invariant parts. Some observations about the cohomology of $J$-modified de Rham complexes are also made.","authors_text":"Tedi Draghici, Weiyi Zhang","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-11-30T19:46:05Z","title":"A note on exact forms on almost complex manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7287","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:aafefb191e0355c406de09873ed7c0e7bd2b52ea90a18415a05cbfbb3c32a875","target":"record","created_at":"2026-05-18T04:07:18Z","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":"fb257d580e15eb645489a60f4c75c548668dcd0aaa4f2fd91934651fdbe3d022","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-11-30T19:46:05Z","title_canon_sha256":"5c2f73d01898b2af0e23b91b5618776bc5fb45b64b32ebf2e2ed7588f9c79a78"},"schema_version":"1.0","source":{"id":"1111.7287","kind":"arxiv","version":1}},"canonical_sha256":"6dbb48523858a0d48f8b3c5dcda65c663016bc24cd887fdd5be69c8de1125b57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dbb48523858a0d48f8b3c5dcda65c663016bc24cd887fdd5be69c8de1125b57","first_computed_at":"2026-05-18T04:07:18.212916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:18.212916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oWWczp9eLe2ZkwxaFhREHV4TJg9WbHvvpsUALCNqxvARyUS/qSuvBeLg+52+2SAv+LTT6IyRlKr5Ac3X5FrMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:18.213767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.7287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aafefb191e0355c406de09873ed7c0e7bd2b52ea90a18415a05cbfbb3c32a875","sha256:b3917664e1f39ed565aed2a2711739563736ee351d28bf796f25b9dd24aacba5"],"state_sha256":"6340db23cf8e2b1a6d757ea2c752b6b36ba77d8ef72b7c85e431d3b460f3489d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dErC9Gl9HpRwtG0hQkmrd6WZCNa7E/7gbHO9K5w3/S6as9c/xvZWwUUlo0VumHr+6PJyMGM41nn+EDjHXJftCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:06:35.308586Z","bundle_sha256":"d901704b4ef82087d1ee20b8de9f2f6934e3d97826d42b66cbe7cef1014220a5"}}