{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:6CYGCLBJBJUPMWA4YSK4IO2J4B","short_pith_number":"pith:6CYGCLBJ","canonical_record":{"source":{"id":"math/0107133","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"2001-07-19T12:38:29Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"ff5b8d32f387424f81d9b22d424953ccd704f46c45c6066a4d5e6f22fffd9bba","abstract_canon_sha256":"34050dab7b9126eb16960d38983f0ccaff6af30a6f0aa45de7eb91a22ca80c6b"},"schema_version":"1.0"},"canonical_sha256":"f0b0612c290a68f6581cc495c43b49e04c6cab88d9b66cf86c6ef5ba52f6cd16","source":{"kind":"arxiv","id":"math/0107133","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0107133","created_at":"2026-07-04T14:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0107133v2","created_at":"2026-07-04T14:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0107133","created_at":"2026-07-04T14:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"6CYGCLBJBJUP","created_at":"2026-07-04T14:35:26Z"},{"alias_kind":"pith_short_16","alias_value":"6CYGCLBJBJUPMWA4","created_at":"2026-07-04T14:35:26Z"},{"alias_kind":"pith_short_8","alias_value":"6CYGCLBJ","created_at":"2026-07-04T14:35:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:6CYGCLBJBJUPMWA4YSK4IO2J4B","target":"record","payload":{"canonical_record":{"source":{"id":"math/0107133","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"2001-07-19T12:38:29Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"ff5b8d32f387424f81d9b22d424953ccd704f46c45c6066a4d5e6f22fffd9bba","abstract_canon_sha256":"34050dab7b9126eb16960d38983f0ccaff6af30a6f0aa45de7eb91a22ca80c6b"},"schema_version":"1.0"},"canonical_sha256":"f0b0612c290a68f6581cc495c43b49e04c6cab88d9b66cf86c6ef5ba52f6cd16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:26.328968Z","signature_b64":"QWhTsHgQQ9j8QDRp+1OSPAubt2/tKZ3ynVwgSkGZVCE03na+5xjZznf1hXIpgIXGeEPgUD5KWaP2LwVRYQP1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0b0612c290a68f6581cc495c43b49e04c6cab88d9b66cf86c6ef5ba52f6cd16","last_reissued_at":"2026-07-04T14:35:26.328548Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:26.328548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0107133","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":"2026-07-04T14:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GnscaYZT0OvZokJCoHiSKbGQAZUwNNM6RthIocRcYKP/S2ucgklGr0DX7+K9F4LooLpCeTwtGlnKeuGsRwCKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:02:33.381203Z"},"content_sha256":"8695e6dc7d4ac35840b99427353a439a4a43335c3a1006827c8f9d3d87d9c777","schema_version":"1.0","event_id":"sha256:8695e6dc7d4ac35840b99427353a439a4a43335c3a1006827c8f9d3d87d9c777"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:6CYGCLBJBJUPMWA4YSK4IO2J4B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poisson geometry with a 3-form background","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.SG","authors_text":"Alan Weinstein, Pavol Severa","submitted_at":"2001-07-19T12:38:29Z","abstract_excerpt":"We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these \"twisted\" Poisson structures are conveniently described as Dirac structures in suitable Courant algebroids. The additive group of 2-forms acts on twisted Poisson structures and permits them to be seen as glued from ordinary Poisson structures defined on local patches. We conclude with remarks on deformation quantization and twisted symplectic groupoids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107133","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/math/0107133/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":"2026-07-04T14:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XsoHLaiQTAK1zy3iqoDAWqGdRLDOFWHZy1pMQclCfzhXUfoIzalOsGfdCxExWWTQK4rT7XAIhK51zMZcktMwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:02:33.381657Z"},"content_sha256":"1a3910e7da7b102c4707be592fe7bc7e1919730a8639496d0da1112c670731ce","schema_version":"1.0","event_id":"sha256:1a3910e7da7b102c4707be592fe7bc7e1919730a8639496d0da1112c670731ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CYGCLBJBJUPMWA4YSK4IO2J4B/bundle.json","state_url":"https://pith.science/pith/6CYGCLBJBJUPMWA4YSK4IO2J4B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CYGCLBJBJUPMWA4YSK4IO2J4B/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":"2026-07-07T11:02:33Z","links":{"resolver":"https://pith.science/pith/6CYGCLBJBJUPMWA4YSK4IO2J4B","bundle":"https://pith.science/pith/6CYGCLBJBJUPMWA4YSK4IO2J4B/bundle.json","state":"https://pith.science/pith/6CYGCLBJBJUPMWA4YSK4IO2J4B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CYGCLBJBJUPMWA4YSK4IO2J4B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:6CYGCLBJBJUPMWA4YSK4IO2J4B","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":"34050dab7b9126eb16960d38983f0ccaff6af30a6f0aa45de7eb91a22ca80c6b","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.SG","submitted_at":"2001-07-19T12:38:29Z","title_canon_sha256":"ff5b8d32f387424f81d9b22d424953ccd704f46c45c6066a4d5e6f22fffd9bba"},"schema_version":"1.0","source":{"id":"math/0107133","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0107133","created_at":"2026-07-04T14:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0107133v2","created_at":"2026-07-04T14:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0107133","created_at":"2026-07-04T14:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"6CYGCLBJBJUP","created_at":"2026-07-04T14:35:26Z"},{"alias_kind":"pith_short_16","alias_value":"6CYGCLBJBJUPMWA4","created_at":"2026-07-04T14:35:26Z"},{"alias_kind":"pith_short_8","alias_value":"6CYGCLBJ","created_at":"2026-07-04T14:35:26Z"}],"graph_snapshots":[{"event_id":"sha256:1a3910e7da7b102c4707be592fe7bc7e1919730a8639496d0da1112c670731ce","target":"graph","created_at":"2026-07-04T14:35:26Z","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/math/0107133/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these \"twisted\" Poisson structures are conveniently described as Dirac structures in suitable Courant algebroids. The additive group of 2-forms acts on twisted Poisson structures and permits them to be seen as glued from ordinary Poisson structures defined on local patches. We conclude with remarks on deformation quantization and twisted symplectic groupoids.","authors_text":"Alan Weinstein, Pavol Severa","cross_cats":["hep-th"],"headline":"","license":"","primary_cat":"math.SG","submitted_at":"2001-07-19T12:38:29Z","title":"Poisson geometry with a 3-form background"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107133","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":"sha256:8695e6dc7d4ac35840b99427353a439a4a43335c3a1006827c8f9d3d87d9c777","target":"record","created_at":"2026-07-04T14:35:26Z","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":"34050dab7b9126eb16960d38983f0ccaff6af30a6f0aa45de7eb91a22ca80c6b","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.SG","submitted_at":"2001-07-19T12:38:29Z","title_canon_sha256":"ff5b8d32f387424f81d9b22d424953ccd704f46c45c6066a4d5e6f22fffd9bba"},"schema_version":"1.0","source":{"id":"math/0107133","kind":"arxiv","version":2}},"canonical_sha256":"f0b0612c290a68f6581cc495c43b49e04c6cab88d9b66cf86c6ef5ba52f6cd16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0b0612c290a68f6581cc495c43b49e04c6cab88d9b66cf86c6ef5ba52f6cd16","first_computed_at":"2026-07-04T14:35:26.328548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:26.328548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QWhTsHgQQ9j8QDRp+1OSPAubt2/tKZ3ynVwgSkGZVCE03na+5xjZznf1hXIpgIXGeEPgUD5KWaP2LwVRYQP1BA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:26.328968Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0107133","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8695e6dc7d4ac35840b99427353a439a4a43335c3a1006827c8f9d3d87d9c777","sha256:1a3910e7da7b102c4707be592fe7bc7e1919730a8639496d0da1112c670731ce"],"state_sha256":"1807e07e3e4c76f5a255c0dd4f11a282a1383d868859187580c7de58751f7c91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T/41Ede0P5LrLqpPt7aASMFhZPqi+WmqPUpqdR/XLh07Ihaow06WfkGLnqsMYpDgCXOCH0KkJyid5pXTi/qNAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T11:02:33.383701Z","bundle_sha256":"1ab4fbbefaf9dacfce50ac05e162eb25c237c582db570694ffb79808b2ad60a6"}}