{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:UBO6JIFIYPRFMWDRWIJXPFI5NQ","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":"9b1ebff4cb4b78fddd32edf1f878c750dbdee12aa067ab30cda2a7dbbcf75dbe","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2021-07-14T00:52:18Z","title_canon_sha256":"aa4f63559eb8979a03cd7337cc9e3ae7204e91427e6d245fc0bb6b1987207456"},"schema_version":"1.0","source":{"id":"2107.06438","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.06438","created_at":"2026-07-05T03:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"2107.06438v2","created_at":"2026-07-05T03:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.06438","created_at":"2026-07-05T03:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"UBO6JIFIYPRF","created_at":"2026-07-05T03:05:52Z"},{"alias_kind":"pith_short_16","alias_value":"UBO6JIFIYPRFMWDR","created_at":"2026-07-05T03:05:52Z"},{"alias_kind":"pith_short_8","alias_value":"UBO6JIFI","created_at":"2026-07-05T03:05:52Z"}],"graph_snapshots":[{"event_id":"sha256:639dac402ee60d251e24d3406c9b0075a42592e8ba72683a3e7342b0ab1b1326","target":"graph","created_at":"2026-07-05T03:05:52Z","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/2107.06438/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $A$ be a noetherian Koszul Artin-Schelter regular algebra, and let $f\\in A_2$ be a central regular element of $A$. The quotient algebra $A/(f)$ is usually called a (noncommutative) quadric hypersurface. In this paper, we use the Clifford deformation to study the quadric hypersurfaces obtained from the tensor products. We introduce a notion of simple graded isolated singularity and proved that, if $B/(g)$ is a simple graded isolated singularity of 0-type, then there is an equivalence of triangulated categories $\\underline{\\text{mcm}}\\,A/(f)\\cong\\underline{\\text{mcm}}\\,(A\\otimes B)/(f+g)$ of","authors_text":"Ji-Wei He, Xin-Chao Ma, Yu Ye","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2021-07-14T00:52:18Z","title":"Generalized Kn\\\"{o}rrer's Periodicity Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.06438","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":"sha256:42c485aab24e77516a1b9376813dc609a231b67ad559fab9bd84f6354b4c96c4","target":"record","created_at":"2026-07-05T03:05:52Z","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":"9b1ebff4cb4b78fddd32edf1f878c750dbdee12aa067ab30cda2a7dbbcf75dbe","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2021-07-14T00:52:18Z","title_canon_sha256":"aa4f63559eb8979a03cd7337cc9e3ae7204e91427e6d245fc0bb6b1987207456"},"schema_version":"1.0","source":{"id":"2107.06438","kind":"arxiv","version":2}},"canonical_sha256":"a05de4a0a8c3e2565871b21377951d6c107fcb3496d26c11103a4c9db31ecc74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a05de4a0a8c3e2565871b21377951d6c107fcb3496d26c11103a4c9db31ecc74","first_computed_at":"2026-07-05T03:05:52.057209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:05:52.057209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/EBpUNHvoZ+ANUTxXmwLS+HPcm1HHUTHEiznewUFHaELeJBFlHYv/8TKlu7u+ZO4YY7nHmHcT8/jvs9LXE4xBg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:05:52.057748Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.06438","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42c485aab24e77516a1b9376813dc609a231b67ad559fab9bd84f6354b4c96c4","sha256:639dac402ee60d251e24d3406c9b0075a42592e8ba72683a3e7342b0ab1b1326"],"state_sha256":"c315a09c81bf2b1b7c811150b7b2c1f6b51182d232aff4d34f77db98178f1344"}