{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3LAQIBEZWV7Z2X7JO54YKCJNOE","short_pith_number":"pith:3LAQIBEZ","canonical_record":{"source":{"id":"1712.01753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-05T16:51:33Z","cross_cats_sorted":[],"title_canon_sha256":"0ef975c3755d9107830b22be7b9a144989b16b0a55ecc276b3c989cb9b9b4a29","abstract_canon_sha256":"8db6d26685afdecdcb319cf4ffdbfe62dfdb2616a31d37fb07c56b7de47df8eb"},"schema_version":"1.0"},"canonical_sha256":"dac1040499b57f9d5fe9777985092d7134e53f2e97acc5d3883d5dd5c39c1e92","source":{"kind":"arxiv","id":"1712.01753","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.01753","created_at":"2026-05-18T00:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1712.01753v1","created_at":"2026-05-18T00:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.01753","created_at":"2026-05-18T00:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"3LAQIBEZWV7Z","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3LAQIBEZWV7Z2X7J","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3LAQIBEZ","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3LAQIBEZWV7Z2X7JO54YKCJNOE","target":"record","payload":{"canonical_record":{"source":{"id":"1712.01753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-05T16:51:33Z","cross_cats_sorted":[],"title_canon_sha256":"0ef975c3755d9107830b22be7b9a144989b16b0a55ecc276b3c989cb9b9b4a29","abstract_canon_sha256":"8db6d26685afdecdcb319cf4ffdbfe62dfdb2616a31d37fb07c56b7de47df8eb"},"schema_version":"1.0"},"canonical_sha256":"dac1040499b57f9d5fe9777985092d7134e53f2e97acc5d3883d5dd5c39c1e92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:47.658699Z","signature_b64":"s5/piqG8w6gSY3eZjBhwO8LO5tIsx/GvidpIj0h/J6DvBAcjHbOnSNUTTsvRdVaaN4PzucKHg7FbBbF99fyFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dac1040499b57f9d5fe9777985092d7134e53f2e97acc5d3883d5dd5c39c1e92","last_reissued_at":"2026-05-18T00:28:47.658028Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:47.658028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.01753","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MH+HCk6IP1wZwmWvhFEcK+uJBNrF1WSifb+AjwedLG92XG2lGc6OEQCeF2zvhg/Fq/c9ROj7Bj3nNnAbftnoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:14:27.913410Z"},"content_sha256":"32bb2a5f962b82aba7d36ee621bc98d254b0ebf7c970ea82126f004fa8841d8d","schema_version":"1.0","event_id":"sha256:32bb2a5f962b82aba7d36ee621bc98d254b0ebf7c970ea82126f004fa8841d8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3LAQIBEZWV7Z2X7JO54YKCJNOE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"De-noetherizing Cohen-Macaulay rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bruce Olberding, Laszlo Fuchs","submitted_at":"2017-12-05T16:51:33Z","abstract_excerpt":"We introduce a new class of commutative {non-noetherian} rings, called $n$-subperfect rings, generalizing the almost perfect rings that have been studied recently by Fuchs-Salce. For an integer $n \\ge 0$, the ring $R$ is $n$-subperfect if every maximal regular sequence in $R$ has length $n$ and the total ring of quotients of $R/I$ for any ideal $I$ generated by a regular sequence is a perfect ring in the sense of Bass. We define an extended Cohen-Macaulay ring as a commutative ring $R$ that has noetherian prime spectrum and each localization $R_M$ at a maximal ideal $M$ is ht($M$)-subperfect. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01753","kind":"arxiv","version":1},"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":"2026-05-18T00:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aFwjHNslMb69gD0fdR3qch6N6vgUCazmidPtPNUHCTNIEGN9DLK+oMiqAKupR3yz6QpT4hD5Pj7UewjKphm7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:14:27.913767Z"},"content_sha256":"68322681c5c82e3593600fedbfa38599c5b0336f19d713a5b0148ddc5bc6f82f","schema_version":"1.0","event_id":"sha256:68322681c5c82e3593600fedbfa38599c5b0336f19d713a5b0148ddc5bc6f82f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LAQIBEZWV7Z2X7JO54YKCJNOE/bundle.json","state_url":"https://pith.science/pith/3LAQIBEZWV7Z2X7JO54YKCJNOE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LAQIBEZWV7Z2X7JO54YKCJNOE/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":"2026-06-01T04:14:28Z","links":{"resolver":"https://pith.science/pith/3LAQIBEZWV7Z2X7JO54YKCJNOE","bundle":"https://pith.science/pith/3LAQIBEZWV7Z2X7JO54YKCJNOE/bundle.json","state":"https://pith.science/pith/3LAQIBEZWV7Z2X7JO54YKCJNOE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LAQIBEZWV7Z2X7JO54YKCJNOE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3LAQIBEZWV7Z2X7JO54YKCJNOE","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":"8db6d26685afdecdcb319cf4ffdbfe62dfdb2616a31d37fb07c56b7de47df8eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-05T16:51:33Z","title_canon_sha256":"0ef975c3755d9107830b22be7b9a144989b16b0a55ecc276b3c989cb9b9b4a29"},"schema_version":"1.0","source":{"id":"1712.01753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.01753","created_at":"2026-05-18T00:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1712.01753v1","created_at":"2026-05-18T00:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.01753","created_at":"2026-05-18T00:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"3LAQIBEZWV7Z","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3LAQIBEZWV7Z2X7J","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3LAQIBEZ","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:68322681c5c82e3593600fedbfa38599c5b0336f19d713a5b0148ddc5bc6f82f","target":"graph","created_at":"2026-05-18T00:28:47Z","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 introduce a new class of commutative {non-noetherian} rings, called $n$-subperfect rings, generalizing the almost perfect rings that have been studied recently by Fuchs-Salce. For an integer $n \\ge 0$, the ring $R$ is $n$-subperfect if every maximal regular sequence in $R$ has length $n$ and the total ring of quotients of $R/I$ for any ideal $I$ generated by a regular sequence is a perfect ring in the sense of Bass. We define an extended Cohen-Macaulay ring as a commutative ring $R$ that has noetherian prime spectrum and each localization $R_M$ at a maximal ideal $M$ is ht($M$)-subperfect. ","authors_text":"Bruce Olberding, Laszlo Fuchs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-05T16:51:33Z","title":"De-noetherizing Cohen-Macaulay rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01753","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":"sha256:32bb2a5f962b82aba7d36ee621bc98d254b0ebf7c970ea82126f004fa8841d8d","target":"record","created_at":"2026-05-18T00:28:47Z","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":"8db6d26685afdecdcb319cf4ffdbfe62dfdb2616a31d37fb07c56b7de47df8eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-12-05T16:51:33Z","title_canon_sha256":"0ef975c3755d9107830b22be7b9a144989b16b0a55ecc276b3c989cb9b9b4a29"},"schema_version":"1.0","source":{"id":"1712.01753","kind":"arxiv","version":1}},"canonical_sha256":"dac1040499b57f9d5fe9777985092d7134e53f2e97acc5d3883d5dd5c39c1e92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dac1040499b57f9d5fe9777985092d7134e53f2e97acc5d3883d5dd5c39c1e92","first_computed_at":"2026-05-18T00:28:47.658028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:47.658028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s5/piqG8w6gSY3eZjBhwO8LO5tIsx/GvidpIj0h/J6DvBAcjHbOnSNUTTsvRdVaaN4PzucKHg7FbBbF99fyFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:47.658699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.01753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32bb2a5f962b82aba7d36ee621bc98d254b0ebf7c970ea82126f004fa8841d8d","sha256:68322681c5c82e3593600fedbfa38599c5b0336f19d713a5b0148ddc5bc6f82f"],"state_sha256":"494d6be5afe6f6d091a731f767f10bcdf2ac43ef62e7cc8b2e8c1d5ef88e8b95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"58OBj61ROS/RUFLa+gMf88Xsvn39xuEYzZBTmgnZ1CLpCfzK5ezPC6V9gHpo68d/7+47T7uYRL1BgNT1UmHQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:14:28.083646Z","bundle_sha256":"11156252548b2dbb261b050597143ba4397f5cbacbdaacb36115030e950c39fe"}}