{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7E2ZLGXIF342KNVSB55DP5A3QQ","short_pith_number":"pith:7E2ZLGXI","canonical_record":{"source":{"id":"1206.3197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-06-14T17:52:44Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"75d2362a6ce13b96cc3fa51c036a3a2440277ed722d90368f39eef51e346d7bb","abstract_canon_sha256":"5d356a90c67552d275c02154e94a6ddaa17a6e9d521c2925822659425b3cf73e"},"schema_version":"1.0"},"canonical_sha256":"f935959ae82ef9a536b20f7a37f41b8421cf0190722920eb83dc56bee941831e","source":{"kind":"arxiv","id":"1206.3197","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3197","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3197v2","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3197","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"7E2ZLGXIF342","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7E2ZLGXIF342KNVS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7E2ZLGXI","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7E2ZLGXIF342KNVSB55DP5A3QQ","target":"record","payload":{"canonical_record":{"source":{"id":"1206.3197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-06-14T17:52:44Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"75d2362a6ce13b96cc3fa51c036a3a2440277ed722d90368f39eef51e346d7bb","abstract_canon_sha256":"5d356a90c67552d275c02154e94a6ddaa17a6e9d521c2925822659425b3cf73e"},"schema_version":"1.0"},"canonical_sha256":"f935959ae82ef9a536b20f7a37f41b8421cf0190722920eb83dc56bee941831e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:43.706521Z","signature_b64":"d7dbk/sKHYJq0vz9/t6xPlV0HkpzkUOltGGMXDJsUs+0Q9v2KB3qAyfplC7hZB1pBoVcMWJtkvObbJpMx+dtCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f935959ae82ef9a536b20f7a37f41b8421cf0190722920eb83dc56bee941831e","last_reissued_at":"2026-05-18T03:21:43.705835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:43.705835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.3197","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":"2026-05-18T03:21:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0TQKNm2TBJ/DPvrx6PJYghV9PKKQF9jkhJpkT646yGMiOv11UBJlYl7SEblOwC9Zu0OrKWJILI7okNxPpo7vDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T05:48:31.216748Z"},"content_sha256":"812514d6be51cadb3c8dcee89975aa9bbdd9419e619ab483445169eba8468f6d","schema_version":"1.0","event_id":"sha256:812514d6be51cadb3c8dcee89975aa9bbdd9419e619ab483445169eba8468f6d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7E2ZLGXIF342KNVSB55DP5A3QQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ulrich ideals and modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.AC","authors_text":"Kazuho Ozeki, Kei-ichi Watanabe, Ken-ichi Yoshida, Ryo Takahashi, Shiro Goto","submitted_at":"2012-06-14T17:52:44Z","abstract_excerpt":"In this paper we study Ulrich ideals of and Ulrich modules over Cohen--Macaulay local rings from various points of view. We determine the structure of minimal free resolutions of Ulrich modules and their associated graded modules, and classify Ulrich ideals of numerical semigroup rings and rings of finite CM-representation type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3197","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":"2026-05-18T03:21:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D4HxqtqSympegrG+fTI8ZSgPFUA21/DwuT6GCUbh/3sLIL6XZ3TVLsovrlO8LpJzwpZ5ymnuqkJa3mZ4Wt26BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T05:48:31.217086Z"},"content_sha256":"ed7a8004346c54f253a481fe5e9f7aaefbab01ddcf6da38ee9ae4a44d429e53b","schema_version":"1.0","event_id":"sha256:ed7a8004346c54f253a481fe5e9f7aaefbab01ddcf6da38ee9ae4a44d429e53b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7E2ZLGXIF342KNVSB55DP5A3QQ/bundle.json","state_url":"https://pith.science/pith/7E2ZLGXIF342KNVSB55DP5A3QQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7E2ZLGXIF342KNVSB55DP5A3QQ/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":"2026-06-21T05:48:31Z","links":{"resolver":"https://pith.science/pith/7E2ZLGXIF342KNVSB55DP5A3QQ","bundle":"https://pith.science/pith/7E2ZLGXIF342KNVSB55DP5A3QQ/bundle.json","state":"https://pith.science/pith/7E2ZLGXIF342KNVSB55DP5A3QQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7E2ZLGXIF342KNVSB55DP5A3QQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7E2ZLGXIF342KNVSB55DP5A3QQ","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":"5d356a90c67552d275c02154e94a6ddaa17a6e9d521c2925822659425b3cf73e","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-06-14T17:52:44Z","title_canon_sha256":"75d2362a6ce13b96cc3fa51c036a3a2440277ed722d90368f39eef51e346d7bb"},"schema_version":"1.0","source":{"id":"1206.3197","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3197","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3197v2","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3197","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"7E2ZLGXIF342","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7E2ZLGXIF342KNVS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7E2ZLGXI","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:ed7a8004346c54f253a481fe5e9f7aaefbab01ddcf6da38ee9ae4a44d429e53b","target":"graph","created_at":"2026-05-18T03:21:43Z","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":"In this paper we study Ulrich ideals of and Ulrich modules over Cohen--Macaulay local rings from various points of view. We determine the structure of minimal free resolutions of Ulrich modules and their associated graded modules, and classify Ulrich ideals of numerical semigroup rings and rings of finite CM-representation type.","authors_text":"Kazuho Ozeki, Kei-ichi Watanabe, Ken-ichi Yoshida, Ryo Takahashi, Shiro Goto","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-06-14T17:52:44Z","title":"Ulrich ideals and modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3197","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":"sha256:812514d6be51cadb3c8dcee89975aa9bbdd9419e619ab483445169eba8468f6d","target":"record","created_at":"2026-05-18T03:21:43Z","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":"5d356a90c67552d275c02154e94a6ddaa17a6e9d521c2925822659425b3cf73e","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-06-14T17:52:44Z","title_canon_sha256":"75d2362a6ce13b96cc3fa51c036a3a2440277ed722d90368f39eef51e346d7bb"},"schema_version":"1.0","source":{"id":"1206.3197","kind":"arxiv","version":2}},"canonical_sha256":"f935959ae82ef9a536b20f7a37f41b8421cf0190722920eb83dc56bee941831e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f935959ae82ef9a536b20f7a37f41b8421cf0190722920eb83dc56bee941831e","first_computed_at":"2026-05-18T03:21:43.705835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:43.705835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d7dbk/sKHYJq0vz9/t6xPlV0HkpzkUOltGGMXDJsUs+0Q9v2KB3qAyfplC7hZB1pBoVcMWJtkvObbJpMx+dtCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:43.706521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3197","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:812514d6be51cadb3c8dcee89975aa9bbdd9419e619ab483445169eba8468f6d","sha256:ed7a8004346c54f253a481fe5e9f7aaefbab01ddcf6da38ee9ae4a44d429e53b"],"state_sha256":"2599ef6da17248984ea6e9855e09a3b2e9db0b9bdd333ca033c0d47f29e10dcd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a7+GgLRdderL/Wk94D3hoIlm1vZn7DMKaOI36VnTMuEhmkGbggpCA3GfJGS3XSfKNiHfaHBMvzjtZU+DErs2AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T05:48:31.218972Z","bundle_sha256":"2f49cc64f6bceb02f7b463307696b257caa97c827471c7f0324037e67d5783fd"}}