{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AGQOXTOJEICYHNSZWE5SKW6P57","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":"0ae9117b4428230661148b81d42ec53510ee8cb52bd7be731866638f4b43b407","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-06T11:49:29Z","title_canon_sha256":"5e1cf426a89d4bf609743a6cabf75d0e460eae88bd3a6a1582ff885d3f553b45"},"schema_version":"1.0","source":{"id":"1311.1360","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1360","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1360v5","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1360","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"pith_short_12","alias_value":"AGQOXTOJEICY","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AGQOXTOJEICYHNSZ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AGQOXTOJ","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:b850c04c80f6e8f4ae8e2effedd2650868ed0dd3c408e9fb23ca9db5855894fa","target":"graph","created_at":"2026-05-18T01:23:48Z","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":"We define prequantization for Dirac manifolds to generalize known procedures for Poisson and (pre) symplectic manifolds by using characteristic distributions obtained from 2-cocycles associated to Dirac structures. Given a Dirac manifold $(M,D)$, we construct Poisson structure on the space of admissible functions on $(M,D)$ and a representation of the Poisson algebra to establish the prequantization condition of $(M,D)$ in terms of a Lie algebroid cohomology. Additional to this, we introduce a polarization for a Dirac manifold $M$ and discuss procedures for quantization in two cases where $M$ ","authors_text":"Yuji Hirota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-06T11:49:29Z","title":"Geometric quantization of Dirac manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1360","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":"sha256:2cea1d061632d453f9e306b24aea574229dd19ac58f37d02d3ed8417b3a27fb4","target":"record","created_at":"2026-05-18T01:23:48Z","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":"0ae9117b4428230661148b81d42ec53510ee8cb52bd7be731866638f4b43b407","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-06T11:49:29Z","title_canon_sha256":"5e1cf426a89d4bf609743a6cabf75d0e460eae88bd3a6a1582ff885d3f553b45"},"schema_version":"1.0","source":{"id":"1311.1360","kind":"arxiv","version":5}},"canonical_sha256":"01a0ebcdc9220583b659b13b255bcfeff53c03b0312b85426b33738b97fdd8f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01a0ebcdc9220583b659b13b255bcfeff53c03b0312b85426b33738b97fdd8f2","first_computed_at":"2026-05-18T01:23:48.494008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:48.494008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1VgioddA144g2CCv7ReLiSO9QFe26UoPnhYoqZ6sL5kvk8414sfwlSpqkkE+YRfUC7Khrd0YBVftn7CifyqfBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:48.494756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1360","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cea1d061632d453f9e306b24aea574229dd19ac58f37d02d3ed8417b3a27fb4","sha256:b850c04c80f6e8f4ae8e2effedd2650868ed0dd3c408e9fb23ca9db5855894fa"],"state_sha256":"ad47fb928c3d6df589c95f2fa955db1d1cf0d0f02b82b5c3160a9cd24f5c3191"}