{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:OG3ZEMIYN74BSX7VU44X4RXKRQ","short_pith_number":"pith:OG3ZEMIY","schema_version":"1.0","canonical_sha256":"71b79231186ff8195ff5a7397e46ea8c09ebd695e41febbd9e8123cd4e776906","source":{"kind":"arxiv","id":"1804.02881","version":1},"attestation_state":"computed","paper":{"title":"On the noncommutative Bondal-Orlov conjecture for some toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Michel Van den Bergh, \\v{S}pela \\v{S}penko, with an appendix by Jason P. Bell","submitted_at":"2018-04-09T09:30:40Z","abstract_excerpt":"We show that all toric noncommutative crepant resolutions (NCCRs) of affine GIT quotients of \"weakly symmetric\" unimodular torus representations are derived equivalent. This yields evidence for a non-commutative extension of a well known conjecture by Bondal and Orlov stating that all crepant resolutions of a Gorenstein singularity are derived equivalent. We prove our result by showing that all toric NCCRs of the affine GIT quotient are derived equivalent to a fixed Deligne-Mumford GIT quotient stack associated to a generic character of the torus. This extends a result by Halpern-Leistner and "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.02881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-09T09:30:40Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"9ae7ecaf16f3c45d0812d7c84828fcc4955d1d4f94cd951f7d6c8673aa1ff6e8","abstract_canon_sha256":"79afb05f37832820fb87de7a2b785e5960509e466571e54e969df56ca46aee17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:58.076771Z","signature_b64":"1o1dmCMlBBPAgd5Tlw+flTCEf0WAJa86yCMjF2lcLFofvDdB8Kwmqebs0/Rnnqhfggf8PIejV/IYjpbp9u8IAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71b79231186ff8195ff5a7397e46ea8c09ebd695e41febbd9e8123cd4e776906","last_reissued_at":"2026-05-18T00:18:58.076076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:58.076076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the noncommutative Bondal-Orlov conjecture for some toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Michel Van den Bergh, \\v{S}pela \\v{S}penko, with an appendix by Jason P. Bell","submitted_at":"2018-04-09T09:30:40Z","abstract_excerpt":"We show that all toric noncommutative crepant resolutions (NCCRs) of affine GIT quotients of \"weakly symmetric\" unimodular torus representations are derived equivalent. This yields evidence for a non-commutative extension of a well known conjecture by Bondal and Orlov stating that all crepant resolutions of a Gorenstein singularity are derived equivalent. We prove our result by showing that all toric NCCRs of the affine GIT quotient are derived equivalent to a fixed Deligne-Mumford GIT quotient stack associated to a generic character of the torus. This extends a result by Halpern-Leistner and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02881","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.02881","created_at":"2026-05-18T00:18:58.076190+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.02881v1","created_at":"2026-05-18T00:18:58.076190+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.02881","created_at":"2026-05-18T00:18:58.076190+00:00"},{"alias_kind":"pith_short_12","alias_value":"OG3ZEMIYN74B","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"OG3ZEMIYN74BSX7V","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"OG3ZEMIY","created_at":"2026-05-18T12:32:43.782077+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OG3ZEMIYN74BSX7VU44X4RXKRQ","json":"https://pith.science/pith/OG3ZEMIYN74BSX7VU44X4RXKRQ.json","graph_json":"https://pith.science/api/pith-number/OG3ZEMIYN74BSX7VU44X4RXKRQ/graph.json","events_json":"https://pith.science/api/pith-number/OG3ZEMIYN74BSX7VU44X4RXKRQ/events.json","paper":"https://pith.science/paper/OG3ZEMIY"},"agent_actions":{"view_html":"https://pith.science/pith/OG3ZEMIYN74BSX7VU44X4RXKRQ","download_json":"https://pith.science/pith/OG3ZEMIYN74BSX7VU44X4RXKRQ.json","view_paper":"https://pith.science/paper/OG3ZEMIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.02881&json=true","fetch_graph":"https://pith.science/api/pith-number/OG3ZEMIYN74BSX7VU44X4RXKRQ/graph.json","fetch_events":"https://pith.science/api/pith-number/OG3ZEMIYN74BSX7VU44X4RXKRQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OG3ZEMIYN74BSX7VU44X4RXKRQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OG3ZEMIYN74BSX7VU44X4RXKRQ/action/storage_attestation","attest_author":"https://pith.science/pith/OG3ZEMIYN74BSX7VU44X4RXKRQ/action/author_attestation","sign_citation":"https://pith.science/pith/OG3ZEMIYN74BSX7VU44X4RXKRQ/action/citation_signature","submit_replication":"https://pith.science/pith/OG3ZEMIYN74BSX7VU44X4RXKRQ/action/replication_record"}},"created_at":"2026-05-18T00:18:58.076190+00:00","updated_at":"2026-05-18T00:18:58.076190+00:00"}