{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4Y3ST7PUIYD3EMYYYZEIPOWZXO","short_pith_number":"pith:4Y3ST7PU","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"},"canonical_sha256":"e63729fdf44607b23318c64887bad9bbb090b50a43c631082cc03ac5523e166d","source":{"kind":"arxiv","id":"1201.3039","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3039","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3039v2","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3039","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"pith_short_12","alias_value":"4Y3ST7PUIYD3","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4Y3ST7PUIYD3EMYY","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4Y3ST7PU","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4Y3ST7PUIYD3EMYYYZEIPOWZXO","target":"record","payload":{"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"},"canonical_sha256":"e63729fdf44607b23318c64887bad9bbb090b50a43c631082cc03ac5523e166d","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"},"source_kind":"arxiv","source_id":"1201.3039","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EaneW/yu8aGQVoPAO/gzLzkcvItEt3uYtGK1yiMf470wgZy2gGkzEQirV+SlswXiSSk1H+f5sKLxcePoWd4ADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:48:17.951370Z"},"content_sha256":"9f4254075e6bcc236af1795f1bf8861438987a56bdee4113b72e82efa8dae372","schema_version":"1.0","event_id":"sha256:9f4254075e6bcc236af1795f1bf8861438987a56bdee4113b72e82efa8dae372"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4Y3ST7PUIYD3EMYYYZEIPOWZXO","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Qi527FDm/BGO4zURu9poioUuFO4XtvVj86ZrGYbZCOxdvG0MGSP8+NWIU/s9S69HafGCYNNKLYO0cc8aWBXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:48:17.952046Z"},"content_sha256":"b0c2fae729f177a0d9e6bdadca31c0295761964d926f4843c09804633a8a640e","schema_version":"1.0","event_id":"sha256:b0c2fae729f177a0d9e6bdadca31c0295761964d926f4843c09804633a8a640e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO/bundle.json","state_url":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T08:48:17Z","links":{"resolver":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO","bundle":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO/bundle.json","state":"https://pith.science/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4Y3ST7PUIYD3EMYYYZEIPOWZXO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4Y3ST7PUIYD3EMYYYZEIPOWZXO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e46eb21bd09ec57f4bb73d32d5d391eeafc4852443c0a3d09d85ac630c3d2d7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-01-14T19:36:15Z","title_canon_sha256":"1e030292c3ecf639d60685c0ac1517c15bfa996853131a7a358ee45e3d304be6"},"schema_version":"1.0","source":{"id":"1201.3039","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3039","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3039v2","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3039","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"pith_short_12","alias_value":"4Y3ST7PUIYD3","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4Y3ST7PUIYD3EMYY","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4Y3ST7PU","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:b0c2fae729f177a0d9e6bdadca31c0295761964d926f4843c09804633a8a640e","target":"graph","created_at":"2026-05-18T03:55:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Benjamin J. Anderson, Sean Sather-Wagstaff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-01-14T19:36:15Z","title":"NAK for Ext and Ascent of module structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3039","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9f4254075e6bcc236af1795f1bf8861438987a56bdee4113b72e82efa8dae372","target":"record","created_at":"2026-05-18T03:55:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e46eb21bd09ec57f4bb73d32d5d391eeafc4852443c0a3d09d85ac630c3d2d7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-01-14T19:36:15Z","title_canon_sha256":"1e030292c3ecf639d60685c0ac1517c15bfa996853131a7a358ee45e3d304be6"},"schema_version":"1.0","source":{"id":"1201.3039","kind":"arxiv","version":2}},"canonical_sha256":"e63729fdf44607b23318c64887bad9bbb090b50a43c631082cc03ac5523e166d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e63729fdf44607b23318c64887bad9bbb090b50a43c631082cc03ac5523e166d","first_computed_at":"2026-05-18T03:55:46.604852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:46.604852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kMGsnqkZCcro3s5XsR0+z/AKNHu8Pk4Ao+TqLQ1UzO5qQq60JMjVL2c/xZuY63Ou0EtnqqCHI2ACEyUNiGmcAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:46.605381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3039","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f4254075e6bcc236af1795f1bf8861438987a56bdee4113b72e82efa8dae372","sha256:b0c2fae729f177a0d9e6bdadca31c0295761964d926f4843c09804633a8a640e"],"state_sha256":"238ea96a4f438f8749560b0546d42e2cd6270517402059b63b0074fa8631fa4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZW1ggOUUsxawP02qDxZH7KdBq4D/ERAYJUewbZio/2lP/2X/lOq9WFj8jO5WMRelVPEhv9Elkdz1NnQge7XBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:48:17.955379Z","bundle_sha256":"816cf4c125a050f28a67c7a5198020165814922457798778d3c79603be10395b"}}