{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SSLLDEWTTKGF7TWC77QH5WBVLF","short_pith_number":"pith:SSLLDEWT","canonical_record":{"source":{"id":"1303.3903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-15T20:49:25Z","cross_cats_sorted":[],"title_canon_sha256":"476ffc4ea27519d8705c9fc11170d56d4088ef16e0efd2efea49cd1665caa9e4","abstract_canon_sha256":"f85c9ca65f067f3c4c2a5045f6f3278938b7baab75d232168c6a33813515f853"},"schema_version":"1.0"},"canonical_sha256":"9496b192d39a8c5fcec2ffe07ed83559588359917a4fc5171e028cc3667a2692","source":{"kind":"arxiv","id":"1303.3903","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3903","created_at":"2026-05-18T03:30:40Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3903v1","created_at":"2026-05-18T03:30:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3903","created_at":"2026-05-18T03:30:40Z"},{"alias_kind":"pith_short_12","alias_value":"SSLLDEWTTKGF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SSLLDEWTTKGF7TWC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SSLLDEWT","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SSLLDEWTTKGF7TWC77QH5WBVLF","target":"record","payload":{"canonical_record":{"source":{"id":"1303.3903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-15T20:49:25Z","cross_cats_sorted":[],"title_canon_sha256":"476ffc4ea27519d8705c9fc11170d56d4088ef16e0efd2efea49cd1665caa9e4","abstract_canon_sha256":"f85c9ca65f067f3c4c2a5045f6f3278938b7baab75d232168c6a33813515f853"},"schema_version":"1.0"},"canonical_sha256":"9496b192d39a8c5fcec2ffe07ed83559588359917a4fc5171e028cc3667a2692","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:40.602724Z","signature_b64":"1D+ctqIpUm0MmdNEe2DZueWPYqqV9rPA4IqogDNP5VxOGznjbbE9gUEHpSj9B0bDCV/JMXguOdyeAACCRyTFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9496b192d39a8c5fcec2ffe07ed83559588359917a4fc5171e028cc3667a2692","last_reissued_at":"2026-05-18T03:30:40.601900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:40.601900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.3903","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":"2026-05-18T03:30:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGC1Sc77Y14Q1L+uNmLu0WXZyfHGbiat9j1GO1H+ppTmQgxyDwLl9JJLterWzmonLgBgVehdUUdPJKKWrbtSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:22:52.538896Z"},"content_sha256":"8cac35fb163d32f6a0da79796fb2b6ccf8252f844344d3012e0e546e3f85a988","schema_version":"1.0","event_id":"sha256:8cac35fb163d32f6a0da79796fb2b6ccf8252f844344d3012e0e546e3f85a988"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SSLLDEWTTKGF7TWC77QH5WBVLF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poisson cohomology and quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Johannes Huebschmann","submitted_at":"2013-03-15T20:49:25Z","abstract_excerpt":"Let R be a commutative ring, and let A be a Poisson algebra over R. We construct an (R,A)-Lie algebra structure, in the sense of Rinehart, on the A-module of K\\\"ahler differentials of A depending naturally on A and the Poisson bracket. This gives rise to suitable algebraic notions of Poisson homology and cohomology for an arbitrary Poisson algebra. A geometric version thereof includes the canonical homology and Poisson cohomology of a Poisson manifold introduced by Brylinski, Koszul, and Lichnerowicz, and absorbes the latter in standard homological algebra by expressing them as Tor and Ext gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3903","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":"2026-05-18T03:30:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sz8CVfR2vcXGYKt7pSIEibYQhDYhZdc9guxCsQjuf1LObTaXTpdJL409d3PzBi7IZGQML8jC3jrKjC5Yl8xvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:22:52.539245Z"},"content_sha256":"85ec0e139ab4a11d1dbe5b43b10b8346d716ba0c4fdaf3c6496940c275abd237","schema_version":"1.0","event_id":"sha256:85ec0e139ab4a11d1dbe5b43b10b8346d716ba0c4fdaf3c6496940c275abd237"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSLLDEWTTKGF7TWC77QH5WBVLF/bundle.json","state_url":"https://pith.science/pith/SSLLDEWTTKGF7TWC77QH5WBVLF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSLLDEWTTKGF7TWC77QH5WBVLF/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":"2026-07-01T12:22:52Z","links":{"resolver":"https://pith.science/pith/SSLLDEWTTKGF7TWC77QH5WBVLF","bundle":"https://pith.science/pith/SSLLDEWTTKGF7TWC77QH5WBVLF/bundle.json","state":"https://pith.science/pith/SSLLDEWTTKGF7TWC77QH5WBVLF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSLLDEWTTKGF7TWC77QH5WBVLF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SSLLDEWTTKGF7TWC77QH5WBVLF","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":"f85c9ca65f067f3c4c2a5045f6f3278938b7baab75d232168c6a33813515f853","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-15T20:49:25Z","title_canon_sha256":"476ffc4ea27519d8705c9fc11170d56d4088ef16e0efd2efea49cd1665caa9e4"},"schema_version":"1.0","source":{"id":"1303.3903","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3903","created_at":"2026-05-18T03:30:40Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3903v1","created_at":"2026-05-18T03:30:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3903","created_at":"2026-05-18T03:30:40Z"},{"alias_kind":"pith_short_12","alias_value":"SSLLDEWTTKGF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SSLLDEWTTKGF7TWC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SSLLDEWT","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:85ec0e139ab4a11d1dbe5b43b10b8346d716ba0c4fdaf3c6496940c275abd237","target":"graph","created_at":"2026-05-18T03:30:40Z","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":"Let R be a commutative ring, and let A be a Poisson algebra over R. We construct an (R,A)-Lie algebra structure, in the sense of Rinehart, on the A-module of K\\\"ahler differentials of A depending naturally on A and the Poisson bracket. This gives rise to suitable algebraic notions of Poisson homology and cohomology for an arbitrary Poisson algebra. A geometric version thereof includes the canonical homology and Poisson cohomology of a Poisson manifold introduced by Brylinski, Koszul, and Lichnerowicz, and absorbes the latter in standard homological algebra by expressing them as Tor and Ext gro","authors_text":"Johannes Huebschmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-15T20:49:25Z","title":"Poisson cohomology and quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3903","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":"sha256:8cac35fb163d32f6a0da79796fb2b6ccf8252f844344d3012e0e546e3f85a988","target":"record","created_at":"2026-05-18T03:30:40Z","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":"f85c9ca65f067f3c4c2a5045f6f3278938b7baab75d232168c6a33813515f853","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-15T20:49:25Z","title_canon_sha256":"476ffc4ea27519d8705c9fc11170d56d4088ef16e0efd2efea49cd1665caa9e4"},"schema_version":"1.0","source":{"id":"1303.3903","kind":"arxiv","version":1}},"canonical_sha256":"9496b192d39a8c5fcec2ffe07ed83559588359917a4fc5171e028cc3667a2692","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9496b192d39a8c5fcec2ffe07ed83559588359917a4fc5171e028cc3667a2692","first_computed_at":"2026-05-18T03:30:40.601900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:40.601900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1D+ctqIpUm0MmdNEe2DZueWPYqqV9rPA4IqogDNP5VxOGznjbbE9gUEHpSj9B0bDCV/JMXguOdyeAACCRyTFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:40.602724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3903","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cac35fb163d32f6a0da79796fb2b6ccf8252f844344d3012e0e546e3f85a988","sha256:85ec0e139ab4a11d1dbe5b43b10b8346d716ba0c4fdaf3c6496940c275abd237"],"state_sha256":"0720fef6340530e8450b3f078e36da9c4286b49e80edaa1d935ddd763206afdd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7e8Ci8aAmTLhkRegUn/tRko6yy02i+lZO0HeEF6os9LbhbT0Oucwkgc2VTCCKN1xMu7loNQ3/qQWbPDMqfhECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T12:22:52.541980Z","bundle_sha256":"52893bac2633c9464b91461a11756877d530c685c89c2690222cdd899be46586"}}