{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:IAIV4CORW2BIL5JHVJDEXXU7KQ","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":"4fb9405696dd1769046dbc86bb8db3cec40022b823ea5655ecd2038a04642a65","cross_cats_sorted":["dg-ga","math.DG","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1997-09-30T21:52:31Z","title_canon_sha256":"2037074281a644518239068a7f20051e532d74d10d6e270239051d170c1d7dff"},"schema_version":"1.0","source":{"id":"q-alg/9709043","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9709043","created_at":"2026-07-04T15:08:19Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9709043v2","created_at":"2026-07-04T15:08:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9709043","created_at":"2026-07-04T15:08:19Z"},{"alias_kind":"pith_short_12","alias_value":"IAIV4CORW2BI","created_at":"2026-07-04T15:08:19Z"},{"alias_kind":"pith_short_16","alias_value":"IAIV4CORW2BIL5JH","created_at":"2026-07-04T15:08:19Z"},{"alias_kind":"pith_short_8","alias_value":"IAIV4COR","created_at":"2026-07-04T15:08:19Z"}],"graph_snapshots":[{"event_id":"sha256:ed1aef69786dd7c3b7045b8c354a2c09acdec94b930f0f19f8fbc00b239c6dea","target":"graph","created_at":"2026-07-04T15:08:19Z","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/q-alg/9709043/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the Hochschild cohomology of the algebra obtained by formal deformation quantization on a symplectic manifold is isomorphic to the formal series with coefficients in the de Rham cohomology of the manifold. The cohomology class obtained by differentiating the star-product with respect to the deformation parameter is seen to be closely related to the characteristic class of the quantization. A fundamental role in the analysis is played by ``quantum Liouville operators,'' which rescale the deformation parameter in the same way in which Liouville vector fields scale the Poisson struct","authors_text":"Alan Weinstein, Ping Xu","cross_cats":["dg-ga","math.DG","math.QA"],"headline":"","license":"","primary_cat":"q-alg","submitted_at":"1997-09-30T21:52:31Z","title":"Hochschild cohomology and characteristic classes for star-products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9709043","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":"sha256:09fe3d2a11839f70febfe179ea57492967fe61ca419c80f1be9cced79b3ec1eb","target":"record","created_at":"2026-07-04T15:08:19Z","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":"4fb9405696dd1769046dbc86bb8db3cec40022b823ea5655ecd2038a04642a65","cross_cats_sorted":["dg-ga","math.DG","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1997-09-30T21:52:31Z","title_canon_sha256":"2037074281a644518239068a7f20051e532d74d10d6e270239051d170c1d7dff"},"schema_version":"1.0","source":{"id":"q-alg/9709043","kind":"arxiv","version":2}},"canonical_sha256":"40115e09d1b68285f527aa464bde9f5411cb6722670afb7a747140fd93dca05e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40115e09d1b68285f527aa464bde9f5411cb6722670afb7a747140fd93dca05e","first_computed_at":"2026-07-04T15:08:19.908663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:08:19.908663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+bVDexp1e8wRHIpa4WKLKFdmoeDB/T5+gfafPLmHi9hoaSAQrMt+lFP2pjaypqNqsHTtg7lIbIzUyI0T+NMvAg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:08:19.909022Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-alg/9709043","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09fe3d2a11839f70febfe179ea57492967fe61ca419c80f1be9cced79b3ec1eb","sha256:ed1aef69786dd7c3b7045b8c354a2c09acdec94b930f0f19f8fbc00b239c6dea"],"state_sha256":"563522980f4aea70ac2bfe3a959234ab6f64783e1968f0bd0f6302b952d66748"}