{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5DY63OKXTUYF4LWMTQPGKXH7VB","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":"1a68d88f1c60acb33d8a4cd93eac7e7f51005a1f6aa9c16baf2cde146a07b0cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-02T16:33:20Z","title_canon_sha256":"7f7942e6498d00f60d0426d2313735e3de56c134bbfc850e869616c0b597110d"},"schema_version":"1.0","source":{"id":"1810.01359","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01359","created_at":"2026-05-18T00:02:54Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01359v2","created_at":"2026-05-18T00:02:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01359","created_at":"2026-05-18T00:02:54Z"},{"alias_kind":"pith_short_12","alias_value":"5DY63OKXTUYF","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5DY63OKXTUYF4LWM","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5DY63OKX","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:602913ad2188167e8ccf27749915a32520965f22ad3db28aa1558ba319d1e1b8","target":"graph","created_at":"2026-05-18T00:02:54Z","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 $(R,m, \\kappa)$ be a local ring. We give a characterization of $R$-modules $M$ whose local cohomology is finite length up to some index in terms of asymptotic vanishing of Koszul cohomology on parameter ideals up to the same index. In particular, we show that a quasi-unmixed module $M$ is asymptotically Cohen-Macaulay if and only if $M$ is Cohen-Macaulay on the punctured spectrum if and only if $\\sup\\{\\ell(H^i(f_1, \\ldots, f_d;M))\\mid \\sqrt{f_1, \\ldots, f_d} = m \\mbox{, } i< d\\}<\\infty$.","authors_text":"Patricia Klein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-02T16:33:20Z","title":"Characterizing finite length local cohomology in terms of bounds on Koszul cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01359","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":"sha256:9c6dbd3984c219e457d2eaee5846d35b7a08c8c4dc4559b10a5b96d829062887","target":"record","created_at":"2026-05-18T00:02:54Z","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":"1a68d88f1c60acb33d8a4cd93eac7e7f51005a1f6aa9c16baf2cde146a07b0cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-02T16:33:20Z","title_canon_sha256":"7f7942e6498d00f60d0426d2313735e3de56c134bbfc850e869616c0b597110d"},"schema_version":"1.0","source":{"id":"1810.01359","kind":"arxiv","version":2}},"canonical_sha256":"e8f1edb9579d305e2ecc9c1e655cffa86a2d12e5d32fa54cff2e1e2ae853a7fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8f1edb9579d305e2ecc9c1e655cffa86a2d12e5d32fa54cff2e1e2ae853a7fc","first_computed_at":"2026-05-18T00:02:54.574457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:54.574457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xCOvlKadUCecmJ/pcpONe5mXp6YSl8Va6zzWsRiKksThPmtNxVG6CxamRnDp/O5pB9jSDloS6oFXlNyUIf3gCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:54.575149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.01359","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c6dbd3984c219e457d2eaee5846d35b7a08c8c4dc4559b10a5b96d829062887","sha256:602913ad2188167e8ccf27749915a32520965f22ad3db28aa1558ba319d1e1b8"],"state_sha256":"f6c677f15430905821764d54c0205ad8cdd5ab64177043646c4727415b7dca7d"}