{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MPBD2J4HNXFL3RQ4QTSXGYMFIW","short_pith_number":"pith:MPBD2J4H","canonical_record":{"source":{"id":"1408.4689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-20T15:06:57Z","cross_cats_sorted":[],"title_canon_sha256":"9cf9686e19461c9c4bf655d99bfad2357eb58319234a1a5408dc1dae0b002081","abstract_canon_sha256":"a1ca7c76f3efe78e161ad07708f52fe51f1d6982318fea8992c83d7cf1842ef3"},"schema_version":"1.0"},"canonical_sha256":"63c23d27876dcabdc61c84e57361854586e2c4755e7009548d4b73b21e6e7440","source":{"kind":"arxiv","id":"1408.4689","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4689","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4689v1","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4689","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"MPBD2J4HNXFL","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MPBD2J4HNXFL3RQ4","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MPBD2J4H","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MPBD2J4HNXFL3RQ4QTSXGYMFIW","target":"record","payload":{"canonical_record":{"source":{"id":"1408.4689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-20T15:06:57Z","cross_cats_sorted":[],"title_canon_sha256":"9cf9686e19461c9c4bf655d99bfad2357eb58319234a1a5408dc1dae0b002081","abstract_canon_sha256":"a1ca7c76f3efe78e161ad07708f52fe51f1d6982318fea8992c83d7cf1842ef3"},"schema_version":"1.0"},"canonical_sha256":"63c23d27876dcabdc61c84e57361854586e2c4755e7009548d4b73b21e6e7440","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:48.361381Z","signature_b64":"0RyrXrksup6jKutYfbLlKsNb/4GEFpWxh5VSqfoslrlOKBDRJI5JyW3KoOK02E4NR+4hHUaVEwnFECxfLHEhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63c23d27876dcabdc61c84e57361854586e2c4755e7009548d4b73b21e6e7440","last_reissued_at":"2026-05-18T02:44:48.361002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:48.361002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.4689","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":"2026-05-18T02:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lVbGgGQ1DFueFEb/ZmaqYCGoYkcEmcIXkPE7lB4jF6G4YDks1VVHdyLGtInborCoAsvNlw/OBBo6KHAZLudHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:02:06.388063Z"},"content_sha256":"13ec69ffa43147676e6301861eb2d073f0ded1039e42b58622daa057d5c5f532","schema_version":"1.0","event_id":"sha256:13ec69ffa43147676e6301861eb2d073f0ded1039e42b58622daa057d5c5f532"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MPBD2J4HNXFL3RQ4QTSXGYMFIW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The diffeomorphism type of canonical integrations of Poisson tensors on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"David Mart\\'inez Torres","submitted_at":"2014-08-20T15:06:57Z","abstract_excerpt":"A surface $\\Sigma$ endowed with a Poisson tensor $\\pi$ is known to admit a canonical integration $\\mathcal{G}(\\pi)$, which is a 4-dimensional manifold with a (symplectic) groupoid structure. In this short note we show that when $\\pi$ is not an area form on the 2-sphere, then $\\mathcal{G}(\\pi)$ is diffeomorphic to the cotangent bundle $T^*\\Sigma$, this extending results in \\cite{Ma09} and \\cite{BCST12}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4689","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":"2026-05-18T02:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ai6vA9yQBleyICtDnYrSjyti2or1BzvECLW8ckwDrWr7vVKh0mwLPEWB2EkuDTinWau5dQU8nzXBR+SATY4RCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:02:06.388402Z"},"content_sha256":"399830fc1bf57bc341435babdb0ae87a9a4dbca00a8e2807b2d29d12fe277ee0","schema_version":"1.0","event_id":"sha256:399830fc1bf57bc341435babdb0ae87a9a4dbca00a8e2807b2d29d12fe277ee0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MPBD2J4HNXFL3RQ4QTSXGYMFIW/bundle.json","state_url":"https://pith.science/pith/MPBD2J4HNXFL3RQ4QTSXGYMFIW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MPBD2J4HNXFL3RQ4QTSXGYMFIW/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":"2026-06-27T03:02:06Z","links":{"resolver":"https://pith.science/pith/MPBD2J4HNXFL3RQ4QTSXGYMFIW","bundle":"https://pith.science/pith/MPBD2J4HNXFL3RQ4QTSXGYMFIW/bundle.json","state":"https://pith.science/pith/MPBD2J4HNXFL3RQ4QTSXGYMFIW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MPBD2J4HNXFL3RQ4QTSXGYMFIW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MPBD2J4HNXFL3RQ4QTSXGYMFIW","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":"a1ca7c76f3efe78e161ad07708f52fe51f1d6982318fea8992c83d7cf1842ef3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-20T15:06:57Z","title_canon_sha256":"9cf9686e19461c9c4bf655d99bfad2357eb58319234a1a5408dc1dae0b002081"},"schema_version":"1.0","source":{"id":"1408.4689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4689","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4689v1","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4689","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"MPBD2J4HNXFL","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MPBD2J4HNXFL3RQ4","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MPBD2J4H","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:399830fc1bf57bc341435babdb0ae87a9a4dbca00a8e2807b2d29d12fe277ee0","target":"graph","created_at":"2026-05-18T02:44:48Z","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":"A surface $\\Sigma$ endowed with a Poisson tensor $\\pi$ is known to admit a canonical integration $\\mathcal{G}(\\pi)$, which is a 4-dimensional manifold with a (symplectic) groupoid structure. In this short note we show that when $\\pi$ is not an area form on the 2-sphere, then $\\mathcal{G}(\\pi)$ is diffeomorphic to the cotangent bundle $T^*\\Sigma$, this extending results in \\cite{Ma09} and \\cite{BCST12}.","authors_text":"David Mart\\'inez Torres","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-20T15:06:57Z","title":"The diffeomorphism type of canonical integrations of Poisson tensors on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4689","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":"sha256:13ec69ffa43147676e6301861eb2d073f0ded1039e42b58622daa057d5c5f532","target":"record","created_at":"2026-05-18T02:44:48Z","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":"a1ca7c76f3efe78e161ad07708f52fe51f1d6982318fea8992c83d7cf1842ef3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-20T15:06:57Z","title_canon_sha256":"9cf9686e19461c9c4bf655d99bfad2357eb58319234a1a5408dc1dae0b002081"},"schema_version":"1.0","source":{"id":"1408.4689","kind":"arxiv","version":1}},"canonical_sha256":"63c23d27876dcabdc61c84e57361854586e2c4755e7009548d4b73b21e6e7440","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63c23d27876dcabdc61c84e57361854586e2c4755e7009548d4b73b21e6e7440","first_computed_at":"2026-05-18T02:44:48.361002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:48.361002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0RyrXrksup6jKutYfbLlKsNb/4GEFpWxh5VSqfoslrlOKBDRJI5JyW3KoOK02E4NR+4hHUaVEwnFECxfLHEhBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:48.361381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13ec69ffa43147676e6301861eb2d073f0ded1039e42b58622daa057d5c5f532","sha256:399830fc1bf57bc341435babdb0ae87a9a4dbca00a8e2807b2d29d12fe277ee0"],"state_sha256":"d4ac0bcadbc54f88d3d73a1733d6a0fd7443c09db7a3767115f10b637d6f25eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bnly54rMTn5kziv0yhxjyBz0WWGKDvP06NU/3jpbbf2goxIxip5o6Ef22kxVjFT8uT1wyf62C4AhaFJT+y21Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:02:06.390158Z","bundle_sha256":"51670ee5ed32a7eff7ba12f39e6f9152eb510e240fab661059f9c4f98f043090"}}