{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:WY3DOQZI2HS6FJ5E36OGASFDWO","short_pith_number":"pith:WY3DOQZI","canonical_record":{"source":{"id":"0904.1276","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-04-08T07:41:57Z","cross_cats_sorted":["gr-qc","math-ph","math.GT","math.MP"],"title_canon_sha256":"65114c050d50b08ae76e02e69d1e7e2c11702154b9b3c617a59aaa6cc883db95","abstract_canon_sha256":"31bf4ca406c5f363ee66647853459c320b335ca360f221bfca7adfe3e6fc0614"},"schema_version":"1.0"},"canonical_sha256":"b636374328d1e5e2a7a4df9c6048a3b3a6dbb0c285d76557ab49ded59624aef3","source":{"kind":"arxiv","id":"0904.1276","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.1276","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"0904.1276v5","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.1276","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"WY3DOQZI2HS6","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"WY3DOQZI2HS6FJ5E","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"WY3DOQZI","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:WY3DOQZI2HS6FJ5E36OGASFDWO","target":"record","payload":{"canonical_record":{"source":{"id":"0904.1276","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-04-08T07:41:57Z","cross_cats_sorted":["gr-qc","math-ph","math.GT","math.MP"],"title_canon_sha256":"65114c050d50b08ae76e02e69d1e7e2c11702154b9b3c617a59aaa6cc883db95","abstract_canon_sha256":"31bf4ca406c5f363ee66647853459c320b335ca360f221bfca7adfe3e6fc0614"},"schema_version":"1.0"},"canonical_sha256":"b636374328d1e5e2a7a4df9c6048a3b3a6dbb0c285d76557ab49ded59624aef3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:07.333931Z","signature_b64":"1PLjiXDHwWCo76mrzP9JwZ3jQPNw/ZNbpj51xxm/pDXI2XEg7FvdWtZmg5tTsYpUsh3t4frMY1I6eyGAMgYYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b636374328d1e5e2a7a4df9c6048a3b3a6dbb0c285d76557ab49ded59624aef3","last_reissued_at":"2026-05-18T02:44:07.333478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:07.333478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.1276","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7vXYxtlDKsQM/k1NTnyuTzKmxGbPP1uVRADVWGfoZVTovAaFhBz5ySapI7Izv8f/KRwqiufrviIIcgdf9SZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:53:14.259767Z"},"content_sha256":"cd3df70f28f7dcfd530a37e12764797c1ffd7af8aed676f2825dcd92ee14329b","schema_version":"1.0","event_id":"sha256:cd3df70f28f7dcfd530a37e12764797c1ffd7af8aed676f2825dcd92ee14329b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:WY3DOQZI2HS6FJ5E36OGASFDWO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abelian gerbes, generalized geometries and foliations of small exotic R^4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.GT","math.MP"],"primary_cat":"hep-th","authors_text":"Jerzy Kr\\'ol, Torsten Asselmeyer-Maluga","submitted_at":"2009-04-08T07:41:57Z","abstract_excerpt":"In the paper we prove the existence of the strict but relative relation between small exotic $\\mathbb{R}^{4}$ for a fixed radial family of DeMichelis-Freedman type, and cobordism classes of codimension one foliations of $S^{3}$ distinguished by the Godbillon-Vey invariant, $GV\\in H^{3}(S^{3},\\mathbb{R})$ (represented by a 3-form). This invariant can be integrated to get the Godbillon-Vey number. For a fixed radial family, we will show that the isotopy classes (invariance w.r.t. small diffeomorphisms or coordinate transformations) of all members in this family are distinguished by the Godbillon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1276","kind":"arxiv","version":5},"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":"2026-05-18T02:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uZhejunCV1fBdwm8t9sC2Kp3LsRAGJBWwsXEDqlORNikEM4DG/NfZOPopADmzpdxZGdlkQuuvBLXb1WOwUryCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:53:14.260112Z"},"content_sha256":"e748a1597e6e575c449fbceb3c201ba88945e7fb8f2ca5398a9fa8b614426f2c","schema_version":"1.0","event_id":"sha256:e748a1597e6e575c449fbceb3c201ba88945e7fb8f2ca5398a9fa8b614426f2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WY3DOQZI2HS6FJ5E36OGASFDWO/bundle.json","state_url":"https://pith.science/pith/WY3DOQZI2HS6FJ5E36OGASFDWO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WY3DOQZI2HS6FJ5E36OGASFDWO/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":"2026-06-28T21:53:14Z","links":{"resolver":"https://pith.science/pith/WY3DOQZI2HS6FJ5E36OGASFDWO","bundle":"https://pith.science/pith/WY3DOQZI2HS6FJ5E36OGASFDWO/bundle.json","state":"https://pith.science/pith/WY3DOQZI2HS6FJ5E36OGASFDWO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WY3DOQZI2HS6FJ5E36OGASFDWO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:WY3DOQZI2HS6FJ5E36OGASFDWO","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":"31bf4ca406c5f363ee66647853459c320b335ca360f221bfca7adfe3e6fc0614","cross_cats_sorted":["gr-qc","math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-04-08T07:41:57Z","title_canon_sha256":"65114c050d50b08ae76e02e69d1e7e2c11702154b9b3c617a59aaa6cc883db95"},"schema_version":"1.0","source":{"id":"0904.1276","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.1276","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"0904.1276v5","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.1276","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"WY3DOQZI2HS6","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"WY3DOQZI2HS6FJ5E","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"WY3DOQZI","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:e748a1597e6e575c449fbceb3c201ba88945e7fb8f2ca5398a9fa8b614426f2c","target":"graph","created_at":"2026-05-18T02:44:07Z","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":"In the paper we prove the existence of the strict but relative relation between small exotic $\\mathbb{R}^{4}$ for a fixed radial family of DeMichelis-Freedman type, and cobordism classes of codimension one foliations of $S^{3}$ distinguished by the Godbillon-Vey invariant, $GV\\in H^{3}(S^{3},\\mathbb{R})$ (represented by a 3-form). This invariant can be integrated to get the Godbillon-Vey number. For a fixed radial family, we will show that the isotopy classes (invariance w.r.t. small diffeomorphisms or coordinate transformations) of all members in this family are distinguished by the Godbillon","authors_text":"Jerzy Kr\\'ol, Torsten Asselmeyer-Maluga","cross_cats":["gr-qc","math-ph","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-04-08T07:41:57Z","title":"Abelian gerbes, generalized geometries and foliations of small exotic R^4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1276","kind":"arxiv","version":5},"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:cd3df70f28f7dcfd530a37e12764797c1ffd7af8aed676f2825dcd92ee14329b","target":"record","created_at":"2026-05-18T02:44:07Z","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":"31bf4ca406c5f363ee66647853459c320b335ca360f221bfca7adfe3e6fc0614","cross_cats_sorted":["gr-qc","math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-04-08T07:41:57Z","title_canon_sha256":"65114c050d50b08ae76e02e69d1e7e2c11702154b9b3c617a59aaa6cc883db95"},"schema_version":"1.0","source":{"id":"0904.1276","kind":"arxiv","version":5}},"canonical_sha256":"b636374328d1e5e2a7a4df9c6048a3b3a6dbb0c285d76557ab49ded59624aef3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b636374328d1e5e2a7a4df9c6048a3b3a6dbb0c285d76557ab49ded59624aef3","first_computed_at":"2026-05-18T02:44:07.333478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:07.333478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1PLjiXDHwWCo76mrzP9JwZ3jQPNw/ZNbpj51xxm/pDXI2XEg7FvdWtZmg5tTsYpUsh3t4frMY1I6eyGAMgYYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:07.333931Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.1276","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd3df70f28f7dcfd530a37e12764797c1ffd7af8aed676f2825dcd92ee14329b","sha256:e748a1597e6e575c449fbceb3c201ba88945e7fb8f2ca5398a9fa8b614426f2c"],"state_sha256":"b6ad21ea2960e656e1f1384929251ea1e992b8d0614dd991231a05afa58a0211"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZfVeAIu5dLtGS0RLIQtooT3GB8xl/K82z8OOVLKFJap22CdZKi4lfUy8GqzfYFICA3ecMpkQ+JVI5jrcP9wyBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T21:53:14.261982Z","bundle_sha256":"ef45f608fcd6119b2fd2a48316b325aa3705a437ffe7f366300c1cd4ee15a788"}}