{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WC5X2ES5T2YHPXWLEDGENPSVLX","short_pith_number":"pith:WC5X2ES5","canonical_record":{"source":{"id":"1412.8061","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-27T15:30:18Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"085ad881c7ad3688ca7ef9932729532e0ee9747d095c9115b8b3d06cb9436c11","abstract_canon_sha256":"568613b11ae9912099283970571d36ef6f90c89700e2ff47a302a301e2ddde3a"},"schema_version":"1.0"},"canonical_sha256":"b0bb7d125d9eb077decb20cc46be555df6c860e71e5cfea580b6ea98f09cfabd","source":{"kind":"arxiv","id":"1412.8061","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.8061","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"arxiv_version","alias_value":"1412.8061v2","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8061","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"pith_short_12","alias_value":"WC5X2ES5T2YH","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WC5X2ES5T2YHPXWL","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WC5X2ES5","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WC5X2ES5T2YHPXWLEDGENPSVLX","target":"record","payload":{"canonical_record":{"source":{"id":"1412.8061","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-27T15:30:18Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"085ad881c7ad3688ca7ef9932729532e0ee9747d095c9115b8b3d06cb9436c11","abstract_canon_sha256":"568613b11ae9912099283970571d36ef6f90c89700e2ff47a302a301e2ddde3a"},"schema_version":"1.0"},"canonical_sha256":"b0bb7d125d9eb077decb20cc46be555df6c860e71e5cfea580b6ea98f09cfabd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:31.077582Z","signature_b64":"F9MaxTp9mwFHRNSn5NIwU1NyOhk3/QVcoShq/YCTde7unbBa8lJ6UQwY0Ka3OzLE+suHOxqmZsw2oPptjsdXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0bb7d125d9eb077decb20cc46be555df6c860e71e5cfea580b6ea98f09cfabd","last_reissued_at":"2026-05-18T01:13:31.076864Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:31.076864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.8061","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o0qjlWGDs9DhJADc0mmDsdBqXoFF2/VTw9q3l21Os2kLpZAFNDjQ4YRxYYKwzz5+5H1+AizjiwYGiZTwQwpJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:36:17.074342Z"},"content_sha256":"ae00a25f60f96e0be021056145e29f97cbc0c1d8e521da2ed8a8f5eb725368af","schema_version":"1.0","event_id":"sha256:ae00a25f60f96e0be021056145e29f97cbc0c1d8e521da2ed8a8f5eb725368af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WC5X2ES5T2YHPXWLEDGENPSVLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singularity categories and singular equivalences for resolving subcategories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Hiroki Matsui, Ryo Takahashi","submitted_at":"2014-12-27T15:30:18Z","abstract_excerpt":"Let $\\X$ be a resolving subcategory of an abelian category. In this paper we investigate the singularity category $\\ds(\\underline\\X)=\\db(\\mod\\underline\\X)/\\kb(\\proj(\\mod\\underline\\X))$ of the stable category $\\underline\\X$ of $\\X$. We consider when the singularity category is triangle equivalent to the stable category of Gorenstein projective objects, and when the stable categories of two resolving subcategories have triangle equivalent singularity categories. Applying this to the module category of a Gorenstein ring, we characterize simple hypersurface singularities of type $(\\a_1)$ as comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8061","kind":"arxiv","version":2},"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":"2026-05-18T01:13:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"21OebXmqVejGNSUweAG7VGD18nXNYEziwZjX8mR9zMuiZyLX5tNK3x/scPvsd7+lCjrkdZIXtKLzRJKTISKZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:36:17.074714Z"},"content_sha256":"9e311479ac6ce3d22a49163a0284b33536baae3860597fbae85400cfe4f4dd26","schema_version":"1.0","event_id":"sha256:9e311479ac6ce3d22a49163a0284b33536baae3860597fbae85400cfe4f4dd26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WC5X2ES5T2YHPXWLEDGENPSVLX/bundle.json","state_url":"https://pith.science/pith/WC5X2ES5T2YHPXWLEDGENPSVLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WC5X2ES5T2YHPXWLEDGENPSVLX/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":"2026-06-12T01:36:17Z","links":{"resolver":"https://pith.science/pith/WC5X2ES5T2YHPXWLEDGENPSVLX","bundle":"https://pith.science/pith/WC5X2ES5T2YHPXWLEDGENPSVLX/bundle.json","state":"https://pith.science/pith/WC5X2ES5T2YHPXWLEDGENPSVLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WC5X2ES5T2YHPXWLEDGENPSVLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WC5X2ES5T2YHPXWLEDGENPSVLX","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":"568613b11ae9912099283970571d36ef6f90c89700e2ff47a302a301e2ddde3a","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-27T15:30:18Z","title_canon_sha256":"085ad881c7ad3688ca7ef9932729532e0ee9747d095c9115b8b3d06cb9436c11"},"schema_version":"1.0","source":{"id":"1412.8061","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.8061","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"arxiv_version","alias_value":"1412.8061v2","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8061","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"pith_short_12","alias_value":"WC5X2ES5T2YH","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WC5X2ES5T2YHPXWL","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WC5X2ES5","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:9e311479ac6ce3d22a49163a0284b33536baae3860597fbae85400cfe4f4dd26","target":"graph","created_at":"2026-05-18T01:13:31Z","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":"Let $\\X$ be a resolving subcategory of an abelian category. In this paper we investigate the singularity category $\\ds(\\underline\\X)=\\db(\\mod\\underline\\X)/\\kb(\\proj(\\mod\\underline\\X))$ of the stable category $\\underline\\X$ of $\\X$. We consider when the singularity category is triangle equivalent to the stable category of Gorenstein projective objects, and when the stable categories of two resolving subcategories have triangle equivalent singularity categories. Applying this to the module category of a Gorenstein ring, we characterize simple hypersurface singularities of type $(\\a_1)$ as comple","authors_text":"Hiroki Matsui, Ryo Takahashi","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-27T15:30:18Z","title":"Singularity categories and singular equivalences for resolving subcategories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8061","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:ae00a25f60f96e0be021056145e29f97cbc0c1d8e521da2ed8a8f5eb725368af","target":"record","created_at":"2026-05-18T01:13:31Z","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":"568613b11ae9912099283970571d36ef6f90c89700e2ff47a302a301e2ddde3a","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-27T15:30:18Z","title_canon_sha256":"085ad881c7ad3688ca7ef9932729532e0ee9747d095c9115b8b3d06cb9436c11"},"schema_version":"1.0","source":{"id":"1412.8061","kind":"arxiv","version":2}},"canonical_sha256":"b0bb7d125d9eb077decb20cc46be555df6c860e71e5cfea580b6ea98f09cfabd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0bb7d125d9eb077decb20cc46be555df6c860e71e5cfea580b6ea98f09cfabd","first_computed_at":"2026-05-18T01:13:31.076864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:31.076864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F9MaxTp9mwFHRNSn5NIwU1NyOhk3/QVcoShq/YCTde7unbBa8lJ6UQwY0Ka3OzLE+suHOxqmZsw2oPptjsdXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:31.077582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.8061","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae00a25f60f96e0be021056145e29f97cbc0c1d8e521da2ed8a8f5eb725368af","sha256:9e311479ac6ce3d22a49163a0284b33536baae3860597fbae85400cfe4f4dd26"],"state_sha256":"9e58b34bbbe3f8a343b9f8206039073e304cc069a6006312b6abc213311d8467"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5zjqMO6eJPs/tdBqHKHbI7a3KT7QYmNFsMU0IFmhvghK/C9E4HQQHQPkQLT9OrwffBVV5uUIuksNq0R2UNyJDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T01:36:17.076699Z","bundle_sha256":"f095c95a1c1df9bf24697ceb1cb3daf6d1439b5a02c32de437ac0ceb3b411223"}}