{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:IDVZZOTPI4IHGYRQLE7SYXXBEY","short_pith_number":"pith:IDVZZOTP","schema_version":"1.0","canonical_sha256":"40eb9cba6f4710736230593f2c5ee1261512da36497d27987584ed8b2554b250","source":{"kind":"arxiv","id":"2504.13566","version":1},"attestation_state":"computed","paper":{"title":"Cohomology Vanishing theorems over some rings containing nilpotents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Tony J. Puthenpurakal","submitted_at":"2025-04-18T09:08:45Z","abstract_excerpt":"(1) Let $(A,\\mathfrak{m})$ be complete Noetherian local ring of dimension $d$ and let $P$ be a prime ideal with $G_P(A) = \\bigoplus_{n \\geq 0}P^n/P^{n+1}$ a domain. Fix $r \\geq 1$. If $J$ is a homogeneous ideal of $G_{P^r}(A)$ with $\\text{dim} \\ G_{P^r}(A)/J > 0$ then the local cohomology module $H^d_J(G_{P^r}(A)) = 0$.\n  (2) Let $A = K[[X_1, \\ldots,X_d]]$ and let $\\mathfrak{m} = (X_1, \\ldots, X_d)$. Assume $K$ is separably closed. Fix $r \\geq 1$. Let $J$ be a homogeneous ideal of $G_{\\mathfrak{m}^r}(A)$. We show that local cohomology modules $H^{j}_J(G_{\\mathfrak{m}^r}(A)) = 0$ for $j \\geq d "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2504.13566","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-04-18T09:08:45Z","cross_cats_sorted":[],"title_canon_sha256":"a7b179de6d52a8678a5776e9df45608327d6ac9b4d6dd2c6286e729bd3c788bd","abstract_canon_sha256":"04014e01f3498bcfdd68eb9c1c1a542f15ff14d9ac2de0c2ccfd33d3026ba4e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:50:58.058199Z","signature_b64":"gttFQaF+TRQTLDkvrRTkUr1U75KGSqyXRhqkQz3RXMKw/oTN8HCaKlHW+a1iYflz8pMzFYtFQi+t6M/f7iTiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40eb9cba6f4710736230593f2c5ee1261512da36497d27987584ed8b2554b250","last_reissued_at":"2026-07-05T10:50:58.057615Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:50:58.057615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohomology Vanishing theorems over some rings containing nilpotents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Tony J. Puthenpurakal","submitted_at":"2025-04-18T09:08:45Z","abstract_excerpt":"(1) Let $(A,\\mathfrak{m})$ be complete Noetherian local ring of dimension $d$ and let $P$ be a prime ideal with $G_P(A) = \\bigoplus_{n \\geq 0}P^n/P^{n+1}$ a domain. Fix $r \\geq 1$. If $J$ is a homogeneous ideal of $G_{P^r}(A)$ with $\\text{dim} \\ G_{P^r}(A)/J > 0$ then the local cohomology module $H^d_J(G_{P^r}(A)) = 0$.\n  (2) Let $A = K[[X_1, \\ldots,X_d]]$ and let $\\mathfrak{m} = (X_1, \\ldots, X_d)$. Assume $K$ is separably closed. Fix $r \\geq 1$. Let $J$ be a homogeneous ideal of $G_{\\mathfrak{m}^r}(A)$. We show that local cohomology modules $H^{j}_J(G_{\\mathfrak{m}^r}(A)) = 0$ for $j \\geq d "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.13566","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.13566/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2504.13566","created_at":"2026-07-05T10:50:58.057689+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.13566v1","created_at":"2026-07-05T10:50:58.057689+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.13566","created_at":"2026-07-05T10:50:58.057689+00:00"},{"alias_kind":"pith_short_12","alias_value":"IDVZZOTPI4IH","created_at":"2026-07-05T10:50:58.057689+00:00"},{"alias_kind":"pith_short_16","alias_value":"IDVZZOTPI4IHGYRQ","created_at":"2026-07-05T10:50:58.057689+00:00"},{"alias_kind":"pith_short_8","alias_value":"IDVZZOTP","created_at":"2026-07-05T10:50:58.057689+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IDVZZOTPI4IHGYRQLE7SYXXBEY","json":"https://pith.science/pith/IDVZZOTPI4IHGYRQLE7SYXXBEY.json","graph_json":"https://pith.science/api/pith-number/IDVZZOTPI4IHGYRQLE7SYXXBEY/graph.json","events_json":"https://pith.science/api/pith-number/IDVZZOTPI4IHGYRQLE7SYXXBEY/events.json","paper":"https://pith.science/paper/IDVZZOTP"},"agent_actions":{"view_html":"https://pith.science/pith/IDVZZOTPI4IHGYRQLE7SYXXBEY","download_json":"https://pith.science/pith/IDVZZOTPI4IHGYRQLE7SYXXBEY.json","view_paper":"https://pith.science/paper/IDVZZOTP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.13566&json=true","fetch_graph":"https://pith.science/api/pith-number/IDVZZOTPI4IHGYRQLE7SYXXBEY/graph.json","fetch_events":"https://pith.science/api/pith-number/IDVZZOTPI4IHGYRQLE7SYXXBEY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IDVZZOTPI4IHGYRQLE7SYXXBEY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IDVZZOTPI4IHGYRQLE7SYXXBEY/action/storage_attestation","attest_author":"https://pith.science/pith/IDVZZOTPI4IHGYRQLE7SYXXBEY/action/author_attestation","sign_citation":"https://pith.science/pith/IDVZZOTPI4IHGYRQLE7SYXXBEY/action/citation_signature","submit_replication":"https://pith.science/pith/IDVZZOTPI4IHGYRQLE7SYXXBEY/action/replication_record"}},"created_at":"2026-07-05T10:50:58.057689+00:00","updated_at":"2026-07-05T10:50:58.057689+00:00"}