{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:A26DCKE7X6IC2J5YT3I4DBZLPQ","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":"573db8da17d98614e7c71c575c93d15bf28a36f5117e5b54d6b4da40b2387e1c","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AG","submitted_at":"2005-06-29T15:26:33Z","title_canon_sha256":"afbb206efeb5613975cb2343e7734e6c8c68527751451c1e5fff7e1ff4e0480e"},"schema_version":"1.0","source":{"id":"math/0506603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506603","created_at":"2026-07-04T14:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506603v1","created_at":"2026-07-04T14:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506603","created_at":"2026-07-04T14:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"A26DCKE7X6IC","created_at":"2026-07-04T14:40:11Z"},{"alias_kind":"pith_short_16","alias_value":"A26DCKE7X6IC2J5Y","created_at":"2026-07-04T14:40:11Z"},{"alias_kind":"pith_short_8","alias_value":"A26DCKE7","created_at":"2026-07-04T14:40:11Z"}],"graph_snapshots":[{"event_id":"sha256:315a6f4a0794a405a239d1f0969950ff983eda2c299bf032ad576728d2b2d867","target":"graph","created_at":"2026-07-04T14:40:11Z","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/0506603/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"These Lectures are based on a course on noncommutative geometry given by the author in 2003 at the University of Chicago. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild cohomology, Serre functors, etc. We also discuss many less known as well as some new results, in particular, noncommutative Chern-Weil theory, noncommutative symplectic geometry, noncommutative differential forms and double-tangent bundles.","authors_text":"Victor Ginzburg","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2005-06-29T15:26:33Z","title":"Lectures on Noncommutative Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506603","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":"sha256:8f87a2850421b0639d6c16e9306bae36bfa7ccf4fe374473fc6c38760bba73d6","target":"record","created_at":"2026-07-04T14:40:11Z","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":"573db8da17d98614e7c71c575c93d15bf28a36f5117e5b54d6b4da40b2387e1c","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AG","submitted_at":"2005-06-29T15:26:33Z","title_canon_sha256":"afbb206efeb5613975cb2343e7734e6c8c68527751451c1e5fff7e1ff4e0480e"},"schema_version":"1.0","source":{"id":"math/0506603","kind":"arxiv","version":1}},"canonical_sha256":"06bc31289fbf902d27b89ed1c1872b7c31273e3829faef7b0bfbb0242c50db51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06bc31289fbf902d27b89ed1c1872b7c31273e3829faef7b0bfbb0242c50db51","first_computed_at":"2026-07-04T14:40:11.500257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:40:11.500257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A5vItANX+PRHBUQckFT8Nt616qMsqnmdQTNg1zOGlQ/gKcQceOJAVbHRdYp1RRbmvlPO9RafuBYHcIEQiRKXCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:40:11.500676Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0506603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f87a2850421b0639d6c16e9306bae36bfa7ccf4fe374473fc6c38760bba73d6","sha256:315a6f4a0794a405a239d1f0969950ff983eda2c299bf032ad576728d2b2d867"],"state_sha256":"04b0aff1ee3eab6e00cb9e47a4a25bbab0b02f4d30cabe1a1db37df3fce22e96"}