{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:BBQ2RLLD5QE6PLTGZEBCTNYN3P","short_pith_number":"pith:BBQ2RLLD","canonical_record":{"source":{"id":"math/0502301","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2005-02-15T01:30:35Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"ec764ea3d3ae58725d26a269be976fb6f183c2a2966be30d435be4651c51ccff","abstract_canon_sha256":"bb5bc3f07be69b09363ac835ed88425ddadec639fb131cda3e2f2361ffdf275b"},"schema_version":"1.0"},"canonical_sha256":"0861a8ad63ec09e7ae66c90229b70ddbfbe0832e03f69d9f4ef8fa8980283558","source":{"kind":"arxiv","id":"math/0502301","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502301","created_at":"2026-07-04T14:50:10Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502301v4","created_at":"2026-07-04T14:50:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502301","created_at":"2026-07-04T14:50:10Z"},{"alias_kind":"pith_short_12","alias_value":"BBQ2RLLD5QE6","created_at":"2026-07-04T14:50:10Z"},{"alias_kind":"pith_short_16","alias_value":"BBQ2RLLD5QE6PLTG","created_at":"2026-07-04T14:50:10Z"},{"alias_kind":"pith_short_8","alias_value":"BBQ2RLLD","created_at":"2026-07-04T14:50:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:BBQ2RLLD5QE6PLTGZEBCTNYN3P","target":"record","payload":{"canonical_record":{"source":{"id":"math/0502301","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2005-02-15T01:30:35Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"ec764ea3d3ae58725d26a269be976fb6f183c2a2966be30d435be4651c51ccff","abstract_canon_sha256":"bb5bc3f07be69b09363ac835ed88425ddadec639fb131cda3e2f2361ffdf275b"},"schema_version":"1.0"},"canonical_sha256":"0861a8ad63ec09e7ae66c90229b70ddbfbe0832e03f69d9f4ef8fa8980283558","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:50:10.702951Z","signature_b64":"fpwaw9/E2uyRSFEx2kYhwIhGhr1X+vwvZ7MBXnMeBblxUv8kA3ebEe3MUO7YBIfK9GMOd9KaQJbU1pwLbs5kDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0861a8ad63ec09e7ae66c90229b70ddbfbe0832e03f69d9f4ef8fa8980283558","last_reissued_at":"2026-07-04T14:50:10.702533Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:50:10.702533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0502301","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:50:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w4Rr6xSVgxtYlh/szqABoRPmRO9pI27emWhlaj9o4pkl/N7xuJ2qr9Dw0APhp6vXBDXBwCot47KT1Ns38ljHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T05:50:20.673924Z"},"content_sha256":"2c938690c6f8817d4b77a6b42643aa3c6bfe36cd1c3380ca18b1f7f5853f0e11","schema_version":"1.0","event_id":"sha256:2c938690c6f8817d4b77a6b42643aa3c6bfe36cd1c3380ca18b1f7f5853f0e11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:BBQ2RLLD5QE6PLTGZEBCTNYN3P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative Geometry and Quiver algebras","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AG","authors_text":"Pavel Etingof, Victor Ginzburg, William Crawley-Boevey","submitted_at":"2005-02-15T01:30:35Z","abstract_excerpt":"We develop a new framework for noncommutative differential geometry based on double derivations. This leads to the notion of moment map and of Hamiltonian reduction in noncommutative symplectic geometry. For any smooth associative algebra B, we define its noncommutative cotangent bundle T^*B, which is a basic example of noncommutative symplectic manifold. Applying Hamiltonian reduction to noncommutative cotangent bundles gives an interesting class of associative algebras, P=P(B), that includes preprojective algebras associated with quivers. Our formalism of noncommutative Hamiltonian reduction"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502301","kind":"arxiv","version":4},"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/0502301/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":"2026-07-04T14:50:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N+gxdQ2gziPzQUZHJlwbOxDjP+c76nXu5tOm6r/1DeSHlJMVUd80HiIzPQYI3VaElPQ5IQvpDWpTzjD8k3kQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T05:50:20.674854Z"},"content_sha256":"90bdad28f3118e642e37c55333538525e6fb9835dea2e5568df47733828902e0","schema_version":"1.0","event_id":"sha256:90bdad28f3118e642e37c55333538525e6fb9835dea2e5568df47733828902e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBQ2RLLD5QE6PLTGZEBCTNYN3P/bundle.json","state_url":"https://pith.science/pith/BBQ2RLLD5QE6PLTGZEBCTNYN3P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBQ2RLLD5QE6PLTGZEBCTNYN3P/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":"2026-08-09T05:50:20Z","links":{"resolver":"https://pith.science/pith/BBQ2RLLD5QE6PLTGZEBCTNYN3P","bundle":"https://pith.science/pith/BBQ2RLLD5QE6PLTGZEBCTNYN3P/bundle.json","state":"https://pith.science/pith/BBQ2RLLD5QE6PLTGZEBCTNYN3P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBQ2RLLD5QE6PLTGZEBCTNYN3P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:BBQ2RLLD5QE6PLTGZEBCTNYN3P","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":"bb5bc3f07be69b09363ac835ed88425ddadec639fb131cda3e2f2361ffdf275b","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AG","submitted_at":"2005-02-15T01:30:35Z","title_canon_sha256":"ec764ea3d3ae58725d26a269be976fb6f183c2a2966be30d435be4651c51ccff"},"schema_version":"1.0","source":{"id":"math/0502301","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502301","created_at":"2026-07-04T14:50:10Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502301v4","created_at":"2026-07-04T14:50:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502301","created_at":"2026-07-04T14:50:10Z"},{"alias_kind":"pith_short_12","alias_value":"BBQ2RLLD5QE6","created_at":"2026-07-04T14:50:10Z"},{"alias_kind":"pith_short_16","alias_value":"BBQ2RLLD5QE6PLTG","created_at":"2026-07-04T14:50:10Z"},{"alias_kind":"pith_short_8","alias_value":"BBQ2RLLD","created_at":"2026-07-04T14:50:10Z"}],"graph_snapshots":[{"event_id":"sha256:90bdad28f3118e642e37c55333538525e6fb9835dea2e5568df47733828902e0","target":"graph","created_at":"2026-07-04T14:50:10Z","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/0502301/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a new framework for noncommutative differential geometry based on double derivations. This leads to the notion of moment map and of Hamiltonian reduction in noncommutative symplectic geometry. For any smooth associative algebra B, we define its noncommutative cotangent bundle T^*B, which is a basic example of noncommutative symplectic manifold. Applying Hamiltonian reduction to noncommutative cotangent bundles gives an interesting class of associative algebras, P=P(B), that includes preprojective algebras associated with quivers. Our formalism of noncommutative Hamiltonian reduction","authors_text":"Pavel Etingof, Victor Ginzburg, William Crawley-Boevey","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2005-02-15T01:30:35Z","title":"Noncommutative Geometry and Quiver algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502301","kind":"arxiv","version":4},"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":"sha256:2c938690c6f8817d4b77a6b42643aa3c6bfe36cd1c3380ca18b1f7f5853f0e11","target":"record","created_at":"2026-07-04T14:50:10Z","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":"bb5bc3f07be69b09363ac835ed88425ddadec639fb131cda3e2f2361ffdf275b","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AG","submitted_at":"2005-02-15T01:30:35Z","title_canon_sha256":"ec764ea3d3ae58725d26a269be976fb6f183c2a2966be30d435be4651c51ccff"},"schema_version":"1.0","source":{"id":"math/0502301","kind":"arxiv","version":4}},"canonical_sha256":"0861a8ad63ec09e7ae66c90229b70ddbfbe0832e03f69d9f4ef8fa8980283558","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0861a8ad63ec09e7ae66c90229b70ddbfbe0832e03f69d9f4ef8fa8980283558","first_computed_at":"2026-07-04T14:50:10.702533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:50:10.702533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fpwaw9/E2uyRSFEx2kYhwIhGhr1X+vwvZ7MBXnMeBblxUv8kA3ebEe3MUO7YBIfK9GMOd9KaQJbU1pwLbs5kDw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:50:10.702951Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0502301","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c938690c6f8817d4b77a6b42643aa3c6bfe36cd1c3380ca18b1f7f5853f0e11","sha256:90bdad28f3118e642e37c55333538525e6fb9835dea2e5568df47733828902e0"],"state_sha256":"017a1d4ce4254f7513030332a6d015b8574b6c623d90b2fc1f684772a71ccf5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YZcnIqmHSLDqwAJMYSY+EikkVr36v9UxUuvEWWGxopTvpR1LbJPY8Nb0XXvxtBVs5CDa7UGyeMDV/Otf8OxAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T05:50:20.682091Z","bundle_sha256":"31220c2fbd66b6fd74af8821207737ba0ae007c0c1bff76a6119c548cf36e3ed"}}