{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TFPHUZDKIGQCFNQQATO4JW3PPT","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":"68c68c5279f9b07e3b41c71bc8e4d868f7d19a7f60524f5c56bc738cbcb78618","cross_cats_sorted":["math.AG","math.DG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-08-10T14:52:08Z","title_canon_sha256":"eed56457bdbca97d10dae628cbdee4701eed6b967412a19a1e6ba1efb56c77c8"},"schema_version":"1.0","source":{"id":"2608.09681","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.09681","created_at":"2026-08-11T02:24:48Z"},{"alias_kind":"arxiv_version","alias_value":"2608.09681v1","created_at":"2026-08-11T02:24:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.09681","created_at":"2026-08-11T02:24:48Z"},{"alias_kind":"pith_short_12","alias_value":"TFPHUZDKIGQC","created_at":"2026-08-11T02:24:48Z"},{"alias_kind":"pith_short_16","alias_value":"TFPHUZDKIGQCFNQQ","created_at":"2026-08-11T02:24:48Z"},{"alias_kind":"pith_short_8","alias_value":"TFPHUZDK","created_at":"2026-08-11T02:24:48Z"}],"graph_snapshots":[{"event_id":"sha256:e44b6d8bb3a38d6181e072f738ea93bb139878e5918729666a33660b9564d4c2","target":"graph","created_at":"2026-08-11T02:24:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.09681/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In Weinstein's symplectic \"category\", objects are symplectic manifolds and morphisms are canonical relations, which may not be composable; it is therefore only morally a category. We construct a true differential graded category which is morally dual to Weinstein's \"category\". The objects in this category are prequantum systems, associated to integral symplectic manifolds. The morphisms are a complex of differential forms twisted by a prequantum line bundle. We also consider the cohomology category, which turns out to be an (ordinary) linear category. In each case, Weinstein's morphisms are as","authors_text":"Jonathan Weitsman","cross_cats":["math.AG","math.DG","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-08-10T14:52:08Z","title":"The Dual DG Category to Weinstein's symplectic \"category\" and applications to Geometric Quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09681","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":"sha256:1bdd973e7e1186f1c3dfb03a502ac22b33d3b4f4a687fa29c76a323e39bd6f50","target":"record","created_at":"2026-08-11T02:24:48Z","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":"68c68c5279f9b07e3b41c71bc8e4d868f7d19a7f60524f5c56bc738cbcb78618","cross_cats_sorted":["math.AG","math.DG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-08-10T14:52:08Z","title_canon_sha256":"eed56457bdbca97d10dae628cbdee4701eed6b967412a19a1e6ba1efb56c77c8"},"schema_version":"1.0","source":{"id":"2608.09681","kind":"arxiv","version":1}},"canonical_sha256":"995e7a646a41a022b61004ddc4db6f7cce12ba2c9c91b14b1081ec136d11c3f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"995e7a646a41a022b61004ddc4db6f7cce12ba2c9c91b14b1081ec136d11c3f3","first_computed_at":"2026-08-11T02:24:48.283491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T02:24:48.283491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d09YJFqtO6uTjbFNTFe3yLd/tjKhkbiGe2P4vAd/KPMoeSn1FS4qzdw7dm5WSr6INDGvdGoyE6tAEau+pbVhDw==","signature_status":"signed_v1","signed_at":"2026-08-11T02:24:48.285127Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.09681","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bdd973e7e1186f1c3dfb03a502ac22b33d3b4f4a687fa29c76a323e39bd6f50","sha256:e44b6d8bb3a38d6181e072f738ea93bb139878e5918729666a33660b9564d4c2"],"state_sha256":"585021e1c4f9a4429de0cae650ee10f73867909a9ac72cb73b68e52c0c48f134"}