{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:4Y3ST7PUIYD3EMYYYZEIPOWZXO","short_pith_number":"pith:4Y3ST7PU","schema_version":"1.0","canonical_sha256":"e63729fdf44607b23318c64887bad9bbb090b50a43c631082cc03ac5523e166d","source":{"kind":"arxiv","id":"1201.3039","version":2},"attestation_state":"computed","paper":{"title":"NAK for Ext and Ascent of module structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Benjamin J. Anderson, Sean Sather-Wagstaff","submitted_at":"2012-01-14T19:36:15Z","abstract_excerpt":"We investigate the interplay between properties of Ext modules and ascent of module structures along local ring homomorphisms. Specifically, let f: (R,m,k) -> (S,mS,k) be a flat local ring homomorphism. We show that if M is a finitely generated R-module such that Ext^i(S,M) satisfies NAK (e.g. if Ext^i(S,M) is finitely generated over S) for i=1,...,dim_R(M), then Ext^i(S,M)=0 for all i\\neq 0 and M has an S-module structure that is compatible with its R-module structure via f. We provide explicit computations of Ext^1(S,M) to indicate how large it can be when M does not have a compatible S-modu"},"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":"1201.3039","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-01-14T19:36:15Z","cross_cats_sorted":[],"title_canon_sha256":"1e030292c3ecf639d60685c0ac1517c15bfa996853131a7a358ee45e3d304be6","abstract_canon_sha256":"e46eb21bd09ec57f4bb73d32d5d391eeafc4852443c0a3d09d85ac630c3d2d7d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:46.605381Z","signature_b64":"kMGsnqkZCcro3s5XsR0+z/AKNHu8Pk4Ao+TqLQ1UzO5qQq60JMjVL2c/xZuY63Ou0EtnqqCHI2ACEyUNiGmcAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e63729fdf44607b23318c64887bad9bbb090b50a43c631082cc03ac5523e166d","last_reissued_at":"2026-05-18T03:55:46.604852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:46.604852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"NAK for Ext and Ascent of module structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Benjamin J. Anderson, Sean Sather-Wagstaff","submitted_at":"2012-01-14T19:36:15Z","abstract_excerpt":"We investigate the interplay between properties of Ext modules and ascent of module structures along local ring homomorphisms. Specifically, let f: (R,m,k) -> (S,mS,k) be a flat local ring homomorphism. We show that if M is a finitely generated R-module such that Ext^i(S,M) satisfies NAK (e.g. if Ext^i(S,M) is finitely generated over S) for i=1,...,dim_R(M), then Ext^i(S,M)=0 for all i\\neq 0 and M has an S-module structure that is compatible with its R-module structure via f. We provide explicit computations of Ext^1(S,M) to indicate how large it can be when M does not have a compatible S-modu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3039","kind":"arxiv","version":2},"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":"1201.3039","created_at":"2026-05-18T03:55:46.604937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.3039v2","created_at":"2026-05-18T03:55:46.604937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3039","created_at":"2026-05-18T03:55:46.604937+00:00"},{"alias_kind":"pith_short_12","alias_value":"4Y3ST7PUIYD3","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"4Y3ST7PUIYD3EMYY","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"4Y3ST7PU","created_at":"2026-05-18T12:26:53.410803+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/4Y3ST7PUIYD3EMYYYZEIPOWZXO","json":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO.json","graph_json":"https://pith.science/api/pith-number/4Y3ST7PUIYD3EMYYYZEIPOWZXO/graph.json","events_json":"https://pith.science/api/pith-number/4Y3ST7PUIYD3EMYYYZEIPOWZXO/events.json","paper":"https://pith.science/paper/4Y3ST7PU"},"agent_actions":{"view_html":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO","download_json":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO.json","view_paper":"https://pith.science/paper/4Y3ST7PU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.3039&json=true","fetch_graph":"https://pith.science/api/pith-number/4Y3ST7PUIYD3EMYYYZEIPOWZXO/graph.json","fetch_events":"https://pith.science/api/pith-number/4Y3ST7PUIYD3EMYYYZEIPOWZXO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO/action/storage_attestation","attest_author":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO/action/author_attestation","sign_citation":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO/action/citation_signature","submit_replication":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO/action/replication_record"}},"created_at":"2026-05-18T03:55:46.604937+00:00","updated_at":"2026-05-18T03:55:46.604937+00:00"}