{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2QFPIYBI3H22U4MVQHXS3KIMVY","short_pith_number":"pith:2QFPIYBI","canonical_record":{"source":{"id":"1809.06524","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-09-18T04:19:17Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"9b7062c3138dc770d5c04b788ce5d4e575e4f0a9bbe2bbd9628aa6ee6181c4ad","abstract_canon_sha256":"7d54e57942c80f04f93f451c1a3b9662c021b51ebc8c66d5f96785173e444be1"},"schema_version":"1.0"},"canonical_sha256":"d40af46028d9f5aa719581ef2da90cae1ee61a47b7b908b07ae29c0934eff7c3","source":{"kind":"arxiv","id":"1809.06524","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06524","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06524v3","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06524","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"pith_short_12","alias_value":"2QFPIYBI3H22","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2QFPIYBI3H22U4MV","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2QFPIYBI","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2QFPIYBI3H22U4MVQHXS3KIMVY","target":"record","payload":{"canonical_record":{"source":{"id":"1809.06524","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-09-18T04:19:17Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"9b7062c3138dc770d5c04b788ce5d4e575e4f0a9bbe2bbd9628aa6ee6181c4ad","abstract_canon_sha256":"7d54e57942c80f04f93f451c1a3b9662c021b51ebc8c66d5f96785173e444be1"},"schema_version":"1.0"},"canonical_sha256":"d40af46028d9f5aa719581ef2da90cae1ee61a47b7b908b07ae29c0934eff7c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:34.426438Z","signature_b64":"zdUkGZjuxE5/qGibfwYrsy4tKjtT6j1mxlw5tyXwc4VoVIOytOOLIfgcm+w8nyQOfYqSYINKB6bT3ZroUuoIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d40af46028d9f5aa719581ef2da90cae1ee61a47b7b908b07ae29c0934eff7c3","last_reissued_at":"2026-05-17T23:40:34.425979Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:34.425979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.06524","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HJBcMLxR9kED9EjDg/NqvANenGRTXaq/tfuRgC4cDjYpQLezP6Gp3chFNrl4JJeBq3TxmOjyTY49ctuqvs1dBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:21:46.772798Z"},"content_sha256":"68cd19bd7b5820246884f2f255a5b3f854e6737a7967256155ae0b2355ca76e1","schema_version":"1.0","event_id":"sha256:68cd19bd7b5820246884f2f255a5b3f854e6737a7967256155ae0b2355ca76e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2QFPIYBI3H22U4MVQHXS3KIMVY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative Kn\\\"{o}rrer periodicity and noncommutative Kleinian singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Andrew Conner, Chelsea Walton, Ellen Kirkman, W. Frank Moore","submitted_at":"2018-09-18T04:19:17Z","abstract_excerpt":"We establish a version of Kn\\\"{o}rrer's Periodicity Theorem in the context of noncommutative invariant theory. Namely, let $A$ be a left noetherian AS-regular algebra, let $f$ be a normal and regular element of $A$ of positive degree, and take $B=A/(f)$. Then there exists a bijection between the set of isomorphism classes of indecomposable non-free maximal Cohen-Macaulay modules over $B$ and those over (a noncommutative analog of) its second double branched cover $(B^\\#)^\\#$. Our results use and extend the study of twisted matrix factorizations, which was introduced by the first three authors "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06524","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2MLBqYb1euQCDOS+MORWb1Rk0GWgA2Bmm47Fw+6XHei/2oljUJxUvthpcJcKNoz9W4UR4glthgtld7sx7U57Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:21:46.773408Z"},"content_sha256":"a3015acf9a0ffe5c8bc1eb783e2844463e7675d8e7b8ff38ddea4021a8a957ff","schema_version":"1.0","event_id":"sha256:a3015acf9a0ffe5c8bc1eb783e2844463e7675d8e7b8ff38ddea4021a8a957ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2QFPIYBI3H22U4MVQHXS3KIMVY/bundle.json","state_url":"https://pith.science/pith/2QFPIYBI3H22U4MVQHXS3KIMVY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2QFPIYBI3H22U4MVQHXS3KIMVY/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":"2026-05-28T00:21:46Z","links":{"resolver":"https://pith.science/pith/2QFPIYBI3H22U4MVQHXS3KIMVY","bundle":"https://pith.science/pith/2QFPIYBI3H22U4MVQHXS3KIMVY/bundle.json","state":"https://pith.science/pith/2QFPIYBI3H22U4MVQHXS3KIMVY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2QFPIYBI3H22U4MVQHXS3KIMVY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2QFPIYBI3H22U4MVQHXS3KIMVY","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":"7d54e57942c80f04f93f451c1a3b9662c021b51ebc8c66d5f96785173e444be1","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-09-18T04:19:17Z","title_canon_sha256":"9b7062c3138dc770d5c04b788ce5d4e575e4f0a9bbe2bbd9628aa6ee6181c4ad"},"schema_version":"1.0","source":{"id":"1809.06524","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06524","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06524v3","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06524","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"pith_short_12","alias_value":"2QFPIYBI3H22","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2QFPIYBI3H22U4MV","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2QFPIYBI","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:a3015acf9a0ffe5c8bc1eb783e2844463e7675d8e7b8ff38ddea4021a8a957ff","target":"graph","created_at":"2026-05-17T23:40:34Z","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 establish a version of Kn\\\"{o}rrer's Periodicity Theorem in the context of noncommutative invariant theory. Namely, let $A$ be a left noetherian AS-regular algebra, let $f$ be a normal and regular element of $A$ of positive degree, and take $B=A/(f)$. Then there exists a bijection between the set of isomorphism classes of indecomposable non-free maximal Cohen-Macaulay modules over $B$ and those over (a noncommutative analog of) its second double branched cover $(B^\\#)^\\#$. Our results use and extend the study of twisted matrix factorizations, which was introduced by the first three authors ","authors_text":"Andrew Conner, Chelsea Walton, Ellen Kirkman, W. Frank Moore","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-09-18T04:19:17Z","title":"Noncommutative Kn\\\"{o}rrer periodicity and noncommutative Kleinian singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06524","kind":"arxiv","version":3},"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":"sha256:68cd19bd7b5820246884f2f255a5b3f854e6737a7967256155ae0b2355ca76e1","target":"record","created_at":"2026-05-17T23:40:34Z","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":"7d54e57942c80f04f93f451c1a3b9662c021b51ebc8c66d5f96785173e444be1","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-09-18T04:19:17Z","title_canon_sha256":"9b7062c3138dc770d5c04b788ce5d4e575e4f0a9bbe2bbd9628aa6ee6181c4ad"},"schema_version":"1.0","source":{"id":"1809.06524","kind":"arxiv","version":3}},"canonical_sha256":"d40af46028d9f5aa719581ef2da90cae1ee61a47b7b908b07ae29c0934eff7c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d40af46028d9f5aa719581ef2da90cae1ee61a47b7b908b07ae29c0934eff7c3","first_computed_at":"2026-05-17T23:40:34.425979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:34.425979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zdUkGZjuxE5/qGibfwYrsy4tKjtT6j1mxlw5tyXwc4VoVIOytOOLIfgcm+w8nyQOfYqSYINKB6bT3ZroUuoIDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:34.426438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06524","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68cd19bd7b5820246884f2f255a5b3f854e6737a7967256155ae0b2355ca76e1","sha256:a3015acf9a0ffe5c8bc1eb783e2844463e7675d8e7b8ff38ddea4021a8a957ff"],"state_sha256":"aef36528d752462f41fd08ca6d13fb72c650c58877877c999fbec46a76d79100"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/n93Mvqql3WImnWhp4OZoTQQ35D4LJCg9R69L8j/R6v8fOnbjmNe9DcVZTz0LjxDjyTNDgzD/9mKvQMrjqgkBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:21:46.776334Z","bundle_sha256":"d09f95fa50327bd191f383075f36b7c72df1c64b3b6390482e1d68d2de11be0f"}}