{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3SBODMRMEPJOC7UITXP5YJEABW","short_pith_number":"pith:3SBODMRM","schema_version":"1.0","canonical_sha256":"dc82e1b22c23d2e17e889ddfdc24800dbc83ec1780695cf40f25eedac20eeb73","source":{"kind":"arxiv","id":"1605.09517","version":2},"attestation_state":"computed","paper":{"title":"Functorial Test Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Axel St\\\"abler, Manuel Blickle","submitted_at":"2016-05-31T07:40:46Z","abstract_excerpt":"In this article we introduce a slight modification of the definition of test modules which is an additive functor $\\tau$ on the category of coherent Cartier modules. We show that in many situations this modification agrees with the usual definition of test modules. Furthermore, we show that for a smooth morphism $f \\colon X \\to Y$ of $F$-finite schemes one has a natural isomorphism $f^! \\circ \\tau \\cong \\tau \\circ f^!$. If $f$ is quasi-finite and of finite type we construct a natural transformation $\\tau \\circ f_* \\to f_* \\circ \\tau$."},"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":"1605.09517","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-31T07:40:46Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"8daf958fe6e998754d11b6751141b1152fef1275979065b4f673cc728fe11037","abstract_canon_sha256":"52df1c6c01f5bee75e7b4c20f44eb5094693aa136e80094a824ee65e1e52a874"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:53.641415Z","signature_b64":"N/f9w5iM11V4zEZVaEQw8Fqhil69Q29PR0SUWVNBIB4Jd0e3d9x+TDtb85neplBTMbI6RbNR0E4zX/D6MMpjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc82e1b22c23d2e17e889ddfdc24800dbc83ec1780695cf40f25eedac20eeb73","last_reissued_at":"2026-05-18T01:07:53.640980Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:53.640980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functorial Test Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Axel St\\\"abler, Manuel Blickle","submitted_at":"2016-05-31T07:40:46Z","abstract_excerpt":"In this article we introduce a slight modification of the definition of test modules which is an additive functor $\\tau$ on the category of coherent Cartier modules. We show that in many situations this modification agrees with the usual definition of test modules. Furthermore, we show that for a smooth morphism $f \\colon X \\to Y$ of $F$-finite schemes one has a natural isomorphism $f^! \\circ \\tau \\cong \\tau \\circ f^!$. If $f$ is quasi-finite and of finite type we construct a natural transformation $\\tau \\circ f_* \\to f_* \\circ \\tau$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09517","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":"1605.09517","created_at":"2026-05-18T01:07:53.641043+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.09517v2","created_at":"2026-05-18T01:07:53.641043+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09517","created_at":"2026-05-18T01:07:53.641043+00:00"},{"alias_kind":"pith_short_12","alias_value":"3SBODMRMEPJO","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3SBODMRMEPJOC7UI","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3SBODMRM","created_at":"2026-05-18T12:29:55.572404+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/3SBODMRMEPJOC7UITXP5YJEABW","json":"https://pith.science/pith/3SBODMRMEPJOC7UITXP5YJEABW.json","graph_json":"https://pith.science/api/pith-number/3SBODMRMEPJOC7UITXP5YJEABW/graph.json","events_json":"https://pith.science/api/pith-number/3SBODMRMEPJOC7UITXP5YJEABW/events.json","paper":"https://pith.science/paper/3SBODMRM"},"agent_actions":{"view_html":"https://pith.science/pith/3SBODMRMEPJOC7UITXP5YJEABW","download_json":"https://pith.science/pith/3SBODMRMEPJOC7UITXP5YJEABW.json","view_paper":"https://pith.science/paper/3SBODMRM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.09517&json=true","fetch_graph":"https://pith.science/api/pith-number/3SBODMRMEPJOC7UITXP5YJEABW/graph.json","fetch_events":"https://pith.science/api/pith-number/3SBODMRMEPJOC7UITXP5YJEABW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3SBODMRMEPJOC7UITXP5YJEABW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3SBODMRMEPJOC7UITXP5YJEABW/action/storage_attestation","attest_author":"https://pith.science/pith/3SBODMRMEPJOC7UITXP5YJEABW/action/author_attestation","sign_citation":"https://pith.science/pith/3SBODMRMEPJOC7UITXP5YJEABW/action/citation_signature","submit_replication":"https://pith.science/pith/3SBODMRMEPJOC7UITXP5YJEABW/action/replication_record"}},"created_at":"2026-05-18T01:07:53.641043+00:00","updated_at":"2026-05-18T01:07:53.641043+00:00"}