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For each $i \\in \\mathbb{N}_0$ let $H^i_{R_{+}}(M)$ denote the $i$-th local cohomology module of $M$ with respect to the irrelevant ideal $R_+ = \\bigoplus_{n > 0} R_n$ of $R$, furnished with its natural grading. We study the tame loci $\\ft^i(M)^{\\leq 3}$ at level $i \\in \\mathbb{N}_0$ in codimension $\\leq 3$ of $M$, that is the sets of all primes $\\fp_0 \\subset R_0$ of height $\\leq 3$ such that the graded $R_{\\fp_0}$-modules $H^i_{R_{+}}(M)_{\\fp_0}$ are tame."},"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":"1106.3638","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-18T10:57:13Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8dcaac8e8a407ecdc21955dc8d02a30ca1a39589272705ae45c8576b7cc2215b","abstract_canon_sha256":"01811d22d12f9c3fd27b351dec1e6dfc44a95ce2400401d5da0546b9cd41cb14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:42.593580Z","signature_b64":"P3BjwJKwOad0jZFrmKSHBfmngt58iLT5qLQ053kTxY84QYspcXgiZGDiAqq2MjAB9ojy3p6daqyxkdmoq5aOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e28738cf4c13aa2ce4adbf3da09286a6ea5877fde1969dac7e4b8cf30ed8f142","last_reissued_at":"2026-05-18T04:19:42.593060Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:42.593060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tame Loci of Certain Local Cohomology Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Markus Brodmann, Maryam Jahangiri","submitted_at":"2011-06-18T10:57:13Z","abstract_excerpt":"Let $M$ be a finitely generated graded module over a Noetherian homogeneous ring $R = \\bigoplus_{n \\in \\mathbb{N}_0}R_n$. For each $i \\in \\mathbb{N}_0$ let $H^i_{R_{+}}(M)$ denote the $i$-th local cohomology module of $M$ with respect to the irrelevant ideal $R_+ = \\bigoplus_{n > 0} R_n$ of $R$, furnished with its natural grading. We study the tame loci $\\ft^i(M)^{\\leq 3}$ at level $i \\in \\mathbb{N}_0$ in codimension $\\leq 3$ of $M$, that is the sets of all primes $\\fp_0 \\subset R_0$ of height $\\leq 3$ such that the graded $R_{\\fp_0}$-modules $H^i_{R_{+}}(M)_{\\fp_0}$ are tame."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3638","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1106.3638","created_at":"2026-05-18T04:19:42.593134+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.3638v1","created_at":"2026-05-18T04:19:42.593134+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3638","created_at":"2026-05-18T04:19:42.593134+00:00"},{"alias_kind":"pith_short_12","alias_value":"4KDTRT2MCOVC","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4KDTRT2MCOVCZZFN","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4KDTRT2M","created_at":"2026-05-18T12:26:20.644004+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/4KDTRT2MCOVCZZFNX462BEUGU3","json":"https://pith.science/pith/4KDTRT2MCOVCZZFNX462BEUGU3.json","graph_json":"https://pith.science/api/pith-number/4KDTRT2MCOVCZZFNX462BEUGU3/graph.json","events_json":"https://pith.science/api/pith-number/4KDTRT2MCOVCZZFNX462BEUGU3/events.json","paper":"https://pith.science/paper/4KDTRT2M"},"agent_actions":{"view_html":"https://pith.science/pith/4KDTRT2MCOVCZZFNX462BEUGU3","download_json":"https://pith.science/pith/4KDTRT2MCOVCZZFNX462BEUGU3.json","view_paper":"https://pith.science/paper/4KDTRT2M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.3638&json=true","fetch_graph":"https://pith.science/api/pith-number/4KDTRT2MCOVCZZFNX462BEUGU3/graph.json","fetch_events":"https://pith.science/api/pith-number/4KDTRT2MCOVCZZFNX462BEUGU3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4KDTRT2MCOVCZZFNX462BEUGU3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4KDTRT2MCOVCZZFNX462BEUGU3/action/storage_attestation","attest_author":"https://pith.science/pith/4KDTRT2MCOVCZZFNX462BEUGU3/action/author_attestation","sign_citation":"https://pith.science/pith/4KDTRT2MCOVCZZFNX462BEUGU3/action/citation_signature","submit_replication":"https://pith.science/pith/4KDTRT2MCOVCZZFNX462BEUGU3/action/replication_record"}},"created_at":"2026-05-18T04:19:42.593134+00:00","updated_at":"2026-05-18T04:19:42.593134+00:00"}