{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:F5VEHUXDDO2ZDZJYCPB3EFI2GL","short_pith_number":"pith:F5VEHUXD","canonical_record":{"source":{"id":"2504.16453","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2025-04-23T06:41:47Z","cross_cats_sorted":[],"title_canon_sha256":"1dd23b0caaaffa14f406254e4170e3680ef7eb0cea48458a7eeb0a30fc4c66cb","abstract_canon_sha256":"925cd072ce15b89ee776b70b20e127f8fccb60712749fb3d40288948c795b7b7"},"schema_version":"1.0"},"canonical_sha256":"2f6a43d2e31bb591e53813c3b2151a32f491c38ce9cc8b7810c273f9dc86e000","source":{"kind":"arxiv","id":"2504.16453","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.16453","created_at":"2026-07-05T11:01:35Z"},{"alias_kind":"arxiv_version","alias_value":"2504.16453v2","created_at":"2026-07-05T11:01:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16453","created_at":"2026-07-05T11:01:35Z"},{"alias_kind":"pith_short_12","alias_value":"F5VEHUXDDO2Z","created_at":"2026-07-05T11:01:35Z"},{"alias_kind":"pith_short_16","alias_value":"F5VEHUXDDO2ZDZJY","created_at":"2026-07-05T11:01:35Z"},{"alias_kind":"pith_short_8","alias_value":"F5VEHUXD","created_at":"2026-07-05T11:01:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:F5VEHUXDDO2ZDZJYCPB3EFI2GL","target":"record","payload":{"canonical_record":{"source":{"id":"2504.16453","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2025-04-23T06:41:47Z","cross_cats_sorted":[],"title_canon_sha256":"1dd23b0caaaffa14f406254e4170e3680ef7eb0cea48458a7eeb0a30fc4c66cb","abstract_canon_sha256":"925cd072ce15b89ee776b70b20e127f8fccb60712749fb3d40288948c795b7b7"},"schema_version":"1.0"},"canonical_sha256":"2f6a43d2e31bb591e53813c3b2151a32f491c38ce9cc8b7810c273f9dc86e000","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:01:35.352195Z","signature_b64":"hHLN/fiVJctxgVfxaYbbsnwnJmBczSAyC3R4Vow/hQkDkydV1AUjGsMOE75qEt/Q9WvBZ8aD3XGvKhHo8p9nDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f6a43d2e31bb591e53813c3b2151a32f491c38ce9cc8b7810c273f9dc86e000","last_reissued_at":"2026-07-05T11:01:35.351719Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:01:35.351719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.16453","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:01:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wxmv/suySL9w1ucdAW75GP+QDBEFhmJXRNIjuNN/WJ7yLhhqiTaLz3mcpp4uG2ccQwFkDb5z5j4kJBZl3xYPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:26:37.270785Z"},"content_sha256":"d83b91732eaf31b7fcf33d179ac5b89cd099a2c28d11a6de9da151fee1eaf512","schema_version":"1.0","event_id":"sha256:d83b91732eaf31b7fcf33d179ac5b89cd099a2c28d11a6de9da151fee1eaf512"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:F5VEHUXDDO2ZDZJYCPB3EFI2GL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Foliation de Rham cohomology of generic Reeb foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Yong-Geun Oh","submitted_at":"2025-04-23T06:41:47Z","abstract_excerpt":"In this paper, we prove that there exists a residual subset of contact forms $\\lambda$ (if any) on a compact connected orientable manifold $M$ for which the foliation de Rham cohomology of the associated Reeb foliation $F_\\lambda$ is trivial in that both $H^0(F_\\lambda,{\\mathbb R})$ and $H^1(F_\\lambda,{\\mathbb R})$ are isomorphic to $\\mathbb R$. We also prove the same triviality for a generic choice of contact forms with fixed contact structure $\\xi$. For any choice of $\\lambda$ from the aforementioned residual subset, this cohomological result can be restated as any of the following two equiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16453","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.16453/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:01:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CXkpYlM/mFWEMXJsPWCUgLIR8QOBIrCB2bx4aEBZ7XhJ6+wvl6DkIj9g+TE0+n/G9t3cizMSs2Ze8qpgrM1NBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:26:37.271673Z"},"content_sha256":"c1202cbb33f2ff8fcf2d88c341a6e23e74af49996d155db0deb1b344d02d720f","schema_version":"1.0","event_id":"sha256:c1202cbb33f2ff8fcf2d88c341a6e23e74af49996d155db0deb1b344d02d720f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5VEHUXDDO2ZDZJYCPB3EFI2GL/bundle.json","state_url":"https://pith.science/pith/F5VEHUXDDO2ZDZJYCPB3EFI2GL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5VEHUXDDO2ZDZJYCPB3EFI2GL/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":"2026-08-13T08:26:37Z","links":{"resolver":"https://pith.science/pith/F5VEHUXDDO2ZDZJYCPB3EFI2GL","bundle":"https://pith.science/pith/F5VEHUXDDO2ZDZJYCPB3EFI2GL/bundle.json","state":"https://pith.science/pith/F5VEHUXDDO2ZDZJYCPB3EFI2GL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5VEHUXDDO2ZDZJYCPB3EFI2GL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:F5VEHUXDDO2ZDZJYCPB3EFI2GL","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":"925cd072ce15b89ee776b70b20e127f8fccb60712749fb3d40288948c795b7b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2025-04-23T06:41:47Z","title_canon_sha256":"1dd23b0caaaffa14f406254e4170e3680ef7eb0cea48458a7eeb0a30fc4c66cb"},"schema_version":"1.0","source":{"id":"2504.16453","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.16453","created_at":"2026-07-05T11:01:35Z"},{"alias_kind":"arxiv_version","alias_value":"2504.16453v2","created_at":"2026-07-05T11:01:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16453","created_at":"2026-07-05T11:01:35Z"},{"alias_kind":"pith_short_12","alias_value":"F5VEHUXDDO2Z","created_at":"2026-07-05T11:01:35Z"},{"alias_kind":"pith_short_16","alias_value":"F5VEHUXDDO2ZDZJY","created_at":"2026-07-05T11:01:35Z"},{"alias_kind":"pith_short_8","alias_value":"F5VEHUXD","created_at":"2026-07-05T11:01:35Z"}],"graph_snapshots":[{"event_id":"sha256:c1202cbb33f2ff8fcf2d88c341a6e23e74af49996d155db0deb1b344d02d720f","target":"graph","created_at":"2026-07-05T11:01:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.16453/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that there exists a residual subset of contact forms $\\lambda$ (if any) on a compact connected orientable manifold $M$ for which the foliation de Rham cohomology of the associated Reeb foliation $F_\\lambda$ is trivial in that both $H^0(F_\\lambda,{\\mathbb R})$ and $H^1(F_\\lambda,{\\mathbb R})$ are isomorphic to $\\mathbb R$. We also prove the same triviality for a generic choice of contact forms with fixed contact structure $\\xi$. For any choice of $\\lambda$ from the aforementioned residual subset, this cohomological result can be restated as any of the following two equiv","authors_text":"Yong-Geun Oh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2025-04-23T06:41:47Z","title":"Foliation de Rham cohomology of generic Reeb foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16453","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:d83b91732eaf31b7fcf33d179ac5b89cd099a2c28d11a6de9da151fee1eaf512","target":"record","created_at":"2026-07-05T11:01:35Z","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":"925cd072ce15b89ee776b70b20e127f8fccb60712749fb3d40288948c795b7b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2025-04-23T06:41:47Z","title_canon_sha256":"1dd23b0caaaffa14f406254e4170e3680ef7eb0cea48458a7eeb0a30fc4c66cb"},"schema_version":"1.0","source":{"id":"2504.16453","kind":"arxiv","version":2}},"canonical_sha256":"2f6a43d2e31bb591e53813c3b2151a32f491c38ce9cc8b7810c273f9dc86e000","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f6a43d2e31bb591e53813c3b2151a32f491c38ce9cc8b7810c273f9dc86e000","first_computed_at":"2026-07-05T11:01:35.351719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:01:35.351719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hHLN/fiVJctxgVfxaYbbsnwnJmBczSAyC3R4Vow/hQkDkydV1AUjGsMOE75qEt/Q9WvBZ8aD3XGvKhHo8p9nDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:01:35.352195Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.16453","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d83b91732eaf31b7fcf33d179ac5b89cd099a2c28d11a6de9da151fee1eaf512","sha256:c1202cbb33f2ff8fcf2d88c341a6e23e74af49996d155db0deb1b344d02d720f"],"state_sha256":"3ace06f943b6b3ad240d65dca5d513f28b1b1510b8b99eabb82105b3ce9ad1ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"miI4c/CaoPx7mMOauNxzpPFDNqPAlRvvob7HzDY5HDyjPMT/lvxwi5OzCN12zkzRpfCf/+CVLoGrJ0jhQyJ7AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T08:26:37.277743Z","bundle_sha256":"33f98085152367baa95b2c26213847f21b3681237b721d43b1f7ec4ec2e4d0fc"}}