{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6DYTIWBOOEQSMNFSKOKLJVPRRE","short_pith_number":"pith:6DYTIWBO","canonical_record":{"source":{"id":"1003.0265","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-03-01T07:25:47Z","cross_cats_sorted":[],"title_canon_sha256":"8a8d19f2d3de593464b261c033f8e81b7b5d395932f1dc1cbf437846e8283d1d","abstract_canon_sha256":"633f0fc75c42b0cb0afa9f3204b8e877952b736795c836c4c0e0eea09c75895b"},"schema_version":"1.0"},"canonical_sha256":"f0f134582e71212634b25394b4d5f1893c188096871abb46068300b113f122f5","source":{"kind":"arxiv","id":"1003.0265","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0265","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0265v3","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0265","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"6DYTIWBOOEQS","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6DYTIWBOOEQSMNFS","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6DYTIWBO","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6DYTIWBOOEQSMNFSKOKLJVPRRE","target":"record","payload":{"canonical_record":{"source":{"id":"1003.0265","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-03-01T07:25:47Z","cross_cats_sorted":[],"title_canon_sha256":"8a8d19f2d3de593464b261c033f8e81b7b5d395932f1dc1cbf437846e8283d1d","abstract_canon_sha256":"633f0fc75c42b0cb0afa9f3204b8e877952b736795c836c4c0e0eea09c75895b"},"schema_version":"1.0"},"canonical_sha256":"f0f134582e71212634b25394b4d5f1893c188096871abb46068300b113f122f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:47:09.050763Z","signature_b64":"goR2EN5eysFwHCaZeUGTgsNnvHTlrYnvtV+rLXQxWRfL80T9E29IVidZOs7xrRzW8bYEArKxkdibenlOe8OGDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0f134582e71212634b25394b4d5f1893c188096871abb46068300b113f122f5","last_reissued_at":"2026-05-18T03:47:09.050306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:47:09.050306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.0265","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":"2026-05-18T03:47:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5wqpUukRL1PC8ALkID302q3vojdhY8axLiwBy7/F+U/RDa8k+uoiTu0oP6HzUWICWGyvn2rJt1eaUIIer5x/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:08:05.608196Z"},"content_sha256":"8706be07459677108e97344d5c2e3b7bf40335921411a962c630a4406aca6f08","schema_version":"1.0","event_id":"sha256:8706be07459677108e97344d5c2e3b7bf40335921411a962c630a4406aca6f08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6DYTIWBOOEQSMNFSKOKLJVPRRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost Cohen-Macaulay and almost regular algebras via almost flat extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kazuma Shimomoto, Mohsen Asgharzadeh","submitted_at":"2010-03-01T07:25:47Z","abstract_excerpt":"The present paper deals with various aspects of the notion of almost Cohen-Macaulay property, which was introduced and studied by Roberts, Singh and Srinivas. We employ the definition of almost zero modules as defined by a value map, which is different from the version of Gabber-Ramero. We prove that, if the local cohomology modules of an algebra $T$ of certain type over a local Noetherian ring are almost zero, $T$ maps to a big Cohen-Macaulay algebra. Then we study how the almost Cohen-Macaulay property behaves under almost faithfully flat extension. As a consequence, we study the structure o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0265","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":"2026-05-18T03:47:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vciiZ51ZKxNr5F/JFaI7u7lVSy/frb7ufG3FAqBzAO+FwWpGvEZonBRJugkN38qKQzKeaqHKzhvWtfdJbnimCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:08:05.608565Z"},"content_sha256":"6967401042ca99370b0f57439bf3ed72af2a3634c4951be3bd147968ba650ac3","schema_version":"1.0","event_id":"sha256:6967401042ca99370b0f57439bf3ed72af2a3634c4951be3bd147968ba650ac3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DYTIWBOOEQSMNFSKOKLJVPRRE/bundle.json","state_url":"https://pith.science/pith/6DYTIWBOOEQSMNFSKOKLJVPRRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DYTIWBOOEQSMNFSKOKLJVPRRE/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":"2026-06-23T15:08:05Z","links":{"resolver":"https://pith.science/pith/6DYTIWBOOEQSMNFSKOKLJVPRRE","bundle":"https://pith.science/pith/6DYTIWBOOEQSMNFSKOKLJVPRRE/bundle.json","state":"https://pith.science/pith/6DYTIWBOOEQSMNFSKOKLJVPRRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DYTIWBOOEQSMNFSKOKLJVPRRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6DYTIWBOOEQSMNFSKOKLJVPRRE","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":"633f0fc75c42b0cb0afa9f3204b8e877952b736795c836c4c0e0eea09c75895b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-03-01T07:25:47Z","title_canon_sha256":"8a8d19f2d3de593464b261c033f8e81b7b5d395932f1dc1cbf437846e8283d1d"},"schema_version":"1.0","source":{"id":"1003.0265","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0265","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0265v3","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0265","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"6DYTIWBOOEQS","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6DYTIWBOOEQSMNFS","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6DYTIWBO","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:6967401042ca99370b0f57439bf3ed72af2a3634c4951be3bd147968ba650ac3","target":"graph","created_at":"2026-05-18T03:47:09Z","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":"The present paper deals with various aspects of the notion of almost Cohen-Macaulay property, which was introduced and studied by Roberts, Singh and Srinivas. We employ the definition of almost zero modules as defined by a value map, which is different from the version of Gabber-Ramero. We prove that, if the local cohomology modules of an algebra $T$ of certain type over a local Noetherian ring are almost zero, $T$ maps to a big Cohen-Macaulay algebra. Then we study how the almost Cohen-Macaulay property behaves under almost faithfully flat extension. As a consequence, we study the structure o","authors_text":"Kazuma Shimomoto, Mohsen Asgharzadeh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-03-01T07:25:47Z","title":"Almost Cohen-Macaulay and almost regular algebras via almost flat extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0265","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":"sha256:8706be07459677108e97344d5c2e3b7bf40335921411a962c630a4406aca6f08","target":"record","created_at":"2026-05-18T03:47:09Z","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":"633f0fc75c42b0cb0afa9f3204b8e877952b736795c836c4c0e0eea09c75895b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-03-01T07:25:47Z","title_canon_sha256":"8a8d19f2d3de593464b261c033f8e81b7b5d395932f1dc1cbf437846e8283d1d"},"schema_version":"1.0","source":{"id":"1003.0265","kind":"arxiv","version":3}},"canonical_sha256":"f0f134582e71212634b25394b4d5f1893c188096871abb46068300b113f122f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0f134582e71212634b25394b4d5f1893c188096871abb46068300b113f122f5","first_computed_at":"2026-05-18T03:47:09.050306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:09.050306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"goR2EN5eysFwHCaZeUGTgsNnvHTlrYnvtV+rLXQxWRfL80T9E29IVidZOs7xrRzW8bYEArKxkdibenlOe8OGDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:09.050763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.0265","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8706be07459677108e97344d5c2e3b7bf40335921411a962c630a4406aca6f08","sha256:6967401042ca99370b0f57439bf3ed72af2a3634c4951be3bd147968ba650ac3"],"state_sha256":"2a00fcd57fffc0f39904b81aa1b270d42ea111d7787301b81e9052b115e6e419"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PvsbQ2hDOw+kIZCp8IsZNRkysRVGfV9OKIbMrxHNI94D6wAa3eORYY6XZWJ+llLoUIzwZUHIJTYCvBET5ySTCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:08:05.610505Z","bundle_sha256":"f29894bf8e1662be143b71ab2ca5932a42a9bde991c1776f95aa76530ebe7175"}}