{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TGCMRAT2NTTMAC3HPJGZPD22X3","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":"0e3413184c257b9072fcd6b458acc534720ecc63d1fec871ca7fcae4fa4274f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-09-07T04:47:55Z","title_canon_sha256":"b7b1f7d935a86b4bb66ef4b185f54cc2f6669f00abe595d75e000f7939358deb"},"schema_version":"1.0","source":{"id":"1809.02310","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02310","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02310v2","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02310","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"TGCMRAT2NTTM","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TGCMRAT2NTTMAC3H","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TGCMRAT2","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:eaa2dd6be336022d00e951e108ea42081a3a0ecff86d9e9da0d2156078364df1","target":"graph","created_at":"2026-05-17T23:46:55Z","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 $R$ be a standard graded algebra over a field $k$, with irrelevant maximal ideal $\\fm$, and $I$ a homogeneous $R$-ideal. We study the asymptotic vanishing behavior of the graded components of the local cohomology modules $\\{\\HH{i}{\\fm}{R/I^n}\\}_{n\\in \\NN}$ for $i<\\dim R/I$. We show that, when $\\chara k= 0$, $R/I$ is Cohen-Macaulay, and $I$ is a complete intersection locally on $\\Spec R \\setminus\\{\\fm\\}$, the lowest degrees of the modules $\\{\\HH{i}{\\fm}{R/I^n}\\}_{n\\in \\NN}$ are bounded by a linear function whose slope is controlled by the generating degrees of the dual of $I/I^2$. Our resul","authors_text":"Hailong Dao, Jonathan Monta\\~no","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-09-07T04:47:55Z","title":"On asymptotic vanishing behavior of local cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02310","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":"sha256:3ed8533668181eeeef3ff4804cbc024f261be5f2f0cefc7e569df94c42d9f724","target":"record","created_at":"2026-05-17T23:46:55Z","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":"0e3413184c257b9072fcd6b458acc534720ecc63d1fec871ca7fcae4fa4274f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-09-07T04:47:55Z","title_canon_sha256":"b7b1f7d935a86b4bb66ef4b185f54cc2f6669f00abe595d75e000f7939358deb"},"schema_version":"1.0","source":{"id":"1809.02310","kind":"arxiv","version":2}},"canonical_sha256":"9984c8827a6ce6c00b677a4d978f5abee708a451d6b09d313f14f54c5cc000ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9984c8827a6ce6c00b677a4d978f5abee708a451d6b09d313f14f54c5cc000ae","first_computed_at":"2026-05-17T23:46:55.160086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:55.160086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O139aL3Xd34nuFuBMSR7jnBBu0bzRUaPjVrm3nBZyB9iaOC/UpaeD8TpR8ljAryY0D3EpvkTX5GjTRYGHX5pDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:55.160816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02310","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ed8533668181eeeef3ff4804cbc024f261be5f2f0cefc7e569df94c42d9f724","sha256:eaa2dd6be336022d00e951e108ea42081a3a0ecff86d9e9da0d2156078364df1"],"state_sha256":"ba1b52edbb2ea634939f0d49fa45f3e69480f8334444a04e5e45b3c32abb6a65"}