{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BCZXQR3RNPZ6L5HYMJXAL5VP3X","short_pith_number":"pith:BCZXQR3R","schema_version":"1.0","canonical_sha256":"08b37847716bf3e5f4f8626e05f6afdde89bc45d359dfb8ffc38aaf6c9120593","source":{"kind":"arxiv","id":"1611.03910","version":3},"attestation_state":"computed","paper":{"title":"Associated points and integral closure of modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Antoni Rangachev","submitted_at":"2016-11-11T23:34:35Z","abstract_excerpt":"Let $X:=\\mathrm{Spec}(R)$ be an affine Noetherian scheme, and $\\mathcal{M} \\subset \\mathcal{N}$ be a pair of finitely generated $R$-modules. Denote their Rees algebras by $\\mathcal{R}(\\mathcal{M})$ and $\\mathcal{R}(\\mathcal{N})$. Let $\\mathcal{N}^{n}$ be the $n$th homogeneous component of $\\mathcal{R}(\\mathcal{N})$ and let $\\mathcal{M}^{n}$ be the image of the $n$th homegeneous component of $\\mathcal{R}(\\mathcal{M})$ in $\\mathcal{N}^n$. Denote by $\\overline{\\mathcal{M}^{n}}$ be the integral closure of $\\mathcal{M}^{n}$ in $\\mathcal{N}^{n}$. We prove that $\\mathrm{Ass}_{X}(\\mathcal{N}^{n}/\\over"},"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":"1611.03910","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-11T23:34:35Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"f860b0ba3cb85740d3fac3c09a4428a102a91d58e6b24862e2a254da8478c730","abstract_canon_sha256":"11642e58b2f6c968730dda71f7796a7d031d08a71b1b7cc2e0f140611587b8d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:14.755099Z","signature_b64":"4Qod5phySvr/BNEBvuKlO1KSGjujeFsJ9LYRYpEAYAV2pljlbzVIX2NfrE+LMW9cuovyOebAyALdrQ/G9HgGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08b37847716bf3e5f4f8626e05f6afdde89bc45d359dfb8ffc38aaf6c9120593","last_reissued_at":"2026-05-18T00:16:14.754401Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:14.754401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Associated points and integral closure of modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Antoni Rangachev","submitted_at":"2016-11-11T23:34:35Z","abstract_excerpt":"Let $X:=\\mathrm{Spec}(R)$ be an affine Noetherian scheme, and $\\mathcal{M} \\subset \\mathcal{N}$ be a pair of finitely generated $R$-modules. Denote their Rees algebras by $\\mathcal{R}(\\mathcal{M})$ and $\\mathcal{R}(\\mathcal{N})$. Let $\\mathcal{N}^{n}$ be the $n$th homogeneous component of $\\mathcal{R}(\\mathcal{N})$ and let $\\mathcal{M}^{n}$ be the image of the $n$th homegeneous component of $\\mathcal{R}(\\mathcal{M})$ in $\\mathcal{N}^n$. Denote by $\\overline{\\mathcal{M}^{n}}$ be the integral closure of $\\mathcal{M}^{n}$ in $\\mathcal{N}^{n}$. We prove that $\\mathrm{Ass}_{X}(\\mathcal{N}^{n}/\\over"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03910","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.03910","created_at":"2026-05-18T00:16:14.754514+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.03910v3","created_at":"2026-05-18T00:16:14.754514+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03910","created_at":"2026-05-18T00:16:14.754514+00:00"},{"alias_kind":"pith_short_12","alias_value":"BCZXQR3RNPZ6","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"BCZXQR3RNPZ6L5HY","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"BCZXQR3R","created_at":"2026-05-18T12:30:07.202191+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/BCZXQR3RNPZ6L5HYMJXAL5VP3X","json":"https://pith.science/pith/BCZXQR3RNPZ6L5HYMJXAL5VP3X.json","graph_json":"https://pith.science/api/pith-number/BCZXQR3RNPZ6L5HYMJXAL5VP3X/graph.json","events_json":"https://pith.science/api/pith-number/BCZXQR3RNPZ6L5HYMJXAL5VP3X/events.json","paper":"https://pith.science/paper/BCZXQR3R"},"agent_actions":{"view_html":"https://pith.science/pith/BCZXQR3RNPZ6L5HYMJXAL5VP3X","download_json":"https://pith.science/pith/BCZXQR3RNPZ6L5HYMJXAL5VP3X.json","view_paper":"https://pith.science/paper/BCZXQR3R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.03910&json=true","fetch_graph":"https://pith.science/api/pith-number/BCZXQR3RNPZ6L5HYMJXAL5VP3X/graph.json","fetch_events":"https://pith.science/api/pith-number/BCZXQR3RNPZ6L5HYMJXAL5VP3X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BCZXQR3RNPZ6L5HYMJXAL5VP3X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BCZXQR3RNPZ6L5HYMJXAL5VP3X/action/storage_attestation","attest_author":"https://pith.science/pith/BCZXQR3RNPZ6L5HYMJXAL5VP3X/action/author_attestation","sign_citation":"https://pith.science/pith/BCZXQR3RNPZ6L5HYMJXAL5VP3X/action/citation_signature","submit_replication":"https://pith.science/pith/BCZXQR3RNPZ6L5HYMJXAL5VP3X/action/replication_record"}},"created_at":"2026-05-18T00:16:14.754514+00:00","updated_at":"2026-05-18T00:16:14.754514+00:00"}