{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KAI6FOOYTMGBCP5TVZ5JDLUAKW","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":"1574f66424f72df5ed1fb28bc1d0567f35b427b4aa8e034b47d6972ba4004ea6","cross_cats_sorted":["math.AC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-10T13:12:10Z","title_canon_sha256":"3202646a2e4775c160da1e690d7e1c8dca81c983a43e5ca08fa869ffb20dfca1"},"schema_version":"1.0","source":{"id":"1707.02836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02836","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02836v1","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02836","created_at":"2026-05-18T00:40:35Z"},{"alias_kind":"pith_short_12","alias_value":"KAI6FOOYTMGB","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KAI6FOOYTMGBCP5T","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KAI6FOOY","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:92eb8189520fe66b6c82b5bb92efaa7147a684155b3fc45269307784866006a0","target":"graph","created_at":"2026-05-18T00:40:35Z","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"},"paper":{"abstract_excerpt":"We construct Kn\\\"orrer type equivalences outside of the hypersurface case, namely, between singularity categories of cyclic quotient surface singularities and certain finite dimensional local algebras. This generalises Kn\\\"orrer's equivalence for singularities of Dynkin type A (between Krull dimensions $2$ and $0$) and yields many new equivalences between singularity categories of finite dimensional algebras.\n  Our construction uses noncommutative resolutions of singularities, relative singularity categories, and an idea of Hille & Ploog yielding strongly quasi-hereditary algebras which we des","authors_text":"Joseph Karmazyn, Martin Kalck","cross_cats":["math.AC","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-10T13:12:10Z","title":"Noncommutative Kn\\\"orrer type equivalences via noncommutative resolutions of singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02836","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":"sha256:1dccee41d9ce00455e5c419dc1e64080b5964b34397701145be18da7cd79812d","target":"record","created_at":"2026-05-18T00:40:35Z","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":"1574f66424f72df5ed1fb28bc1d0567f35b427b4aa8e034b47d6972ba4004ea6","cross_cats_sorted":["math.AC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-10T13:12:10Z","title_canon_sha256":"3202646a2e4775c160da1e690d7e1c8dca81c983a43e5ca08fa869ffb20dfca1"},"schema_version":"1.0","source":{"id":"1707.02836","kind":"arxiv","version":1}},"canonical_sha256":"5011e2b9d89b0c113fb3ae7a91ae8055a093320ab3935507246aba19dc7e72b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5011e2b9d89b0c113fb3ae7a91ae8055a093320ab3935507246aba19dc7e72b3","first_computed_at":"2026-05-18T00:40:35.673264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:35.673264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2sBUHfZnSgPcSMs8Sf+L3VnLOHk9QHVrhF43TaGFi9KADYD4A39sbX1Db9QkgCbyV4wpPag3BPW52evcWP44CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:35.673996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.02836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dccee41d9ce00455e5c419dc1e64080b5964b34397701145be18da7cd79812d","sha256:92eb8189520fe66b6c82b5bb92efaa7147a684155b3fc45269307784866006a0"],"state_sha256":"b68a562d9d4df2a60d51e58dd025a2f6b582a23841aa34f9df9bb839ff7b74af"}