{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QAW6ZT3LIKTZZBO7C3ISGYOQV6","short_pith_number":"pith:QAW6ZT3L","canonical_record":{"source":{"id":"1402.1333","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-02-06T12:08:32Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0b9d241832fad482f531cf36773599ff15813ba2e88c410db36fb564735f06fb","abstract_canon_sha256":"d8558e194df11d33ac6be084ad20a2d3409f10c843f071145c89015da85efa4f"},"schema_version":"1.0"},"canonical_sha256":"802deccf6b42a79c85df16d12361d0af891fcd74cfeed3620314deecee377cb6","source":{"kind":"arxiv","id":"1402.1333","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1333","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1333v2","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1333","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"QAW6ZT3LIKTZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"QAW6ZT3LIKTZZBO7","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"QAW6ZT3L","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QAW6ZT3LIKTZZBO7C3ISGYOQV6","target":"record","payload":{"canonical_record":{"source":{"id":"1402.1333","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-02-06T12:08:32Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0b9d241832fad482f531cf36773599ff15813ba2e88c410db36fb564735f06fb","abstract_canon_sha256":"d8558e194df11d33ac6be084ad20a2d3409f10c843f071145c89015da85efa4f"},"schema_version":"1.0"},"canonical_sha256":"802deccf6b42a79c85df16d12361d0af891fcd74cfeed3620314deecee377cb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:22.161294Z","signature_b64":"YTHv5urY/DE82fhpc53yQb/1z2+MnlYoUgCem0hV3JuXXVWU3MpUDeKunI/S3GX9MqPeT/F2CrNz79hgrNJ0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"802deccf6b42a79c85df16d12361d0af891fcd74cfeed3620314deecee377cb6","last_reissued_at":"2026-05-18T02:18:22.160645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:22.160645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.1333","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":"2026-05-18T02:18:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aDqdSirJULDqKHvSX1EIXYikz69ouHh190u8KhsxfMy97OFDYLduW7Ik1KpQIeIJJ2s/8kMnpVUBpJnRw9xnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:22:25.402556Z"},"content_sha256":"40448e75054ab7ba52dc91461372b008b50099255e0f95d7da8189ab399e24b3","schema_version":"1.0","event_id":"sha256:40448e75054ab7ba52dc91461372b008b50099255e0f95d7da8189ab399e24b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QAW6ZT3LIKTZZBO7C3ISGYOQV6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bernstein-Sato polynomials and test modules in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Axel St\\\"abler, Manuel Blickle","submitted_at":"2014-02-06T12:08:32Z","abstract_excerpt":"In analogy with the complex analytic case, Musta\\c{t}\\u{a} constructed (a family of) Bernstein-Sato polynomials for the structure sheaf $\\mathcal{O}_X$ and a hypersurface $(f=0)$ in $X$, where $X$ is a regular variety over an $F$-finite field of positive characteristic (see arxiv:0711.3794). He shows that the suitably interpreted zeros of his Bernstein-Sato polynomials correspond to the jumping numbers of the test ideal filtration $\\tau(X,f^t)$. In the present paper we generalize Musta\\c{t}\\u{a}'s construction replacing $\\mathcal{O}_X$ by an arbitrary $F$-regular Cartier module $M$ on $X$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1333","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":"2026-05-18T02:18:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y2AonZQCBnBNe2jutHkO6jLzBbcWcYCHGc3vXXGXdmTopUz9yaoW4dlfBxbtGeTA96EBns8dYfwDeQiYU6/jCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:22:25.403138Z"},"content_sha256":"5d3c1a79d57fb58860767c33987049df8b34ca18d8439860cbb0b61076cc0de2","schema_version":"1.0","event_id":"sha256:5d3c1a79d57fb58860767c33987049df8b34ca18d8439860cbb0b61076cc0de2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QAW6ZT3LIKTZZBO7C3ISGYOQV6/bundle.json","state_url":"https://pith.science/pith/QAW6ZT3LIKTZZBO7C3ISGYOQV6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QAW6ZT3LIKTZZBO7C3ISGYOQV6/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":"2026-06-06T21:22:25Z","links":{"resolver":"https://pith.science/pith/QAW6ZT3LIKTZZBO7C3ISGYOQV6","bundle":"https://pith.science/pith/QAW6ZT3LIKTZZBO7C3ISGYOQV6/bundle.json","state":"https://pith.science/pith/QAW6ZT3LIKTZZBO7C3ISGYOQV6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QAW6ZT3LIKTZZBO7C3ISGYOQV6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QAW6ZT3LIKTZZBO7C3ISGYOQV6","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":"d8558e194df11d33ac6be084ad20a2d3409f10c843f071145c89015da85efa4f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-02-06T12:08:32Z","title_canon_sha256":"0b9d241832fad482f531cf36773599ff15813ba2e88c410db36fb564735f06fb"},"schema_version":"1.0","source":{"id":"1402.1333","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1333","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1333v2","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1333","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"QAW6ZT3LIKTZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"QAW6ZT3LIKTZZBO7","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"QAW6ZT3L","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:5d3c1a79d57fb58860767c33987049df8b34ca18d8439860cbb0b61076cc0de2","target":"graph","created_at":"2026-05-18T02:18:22Z","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":"In analogy with the complex analytic case, Musta\\c{t}\\u{a} constructed (a family of) Bernstein-Sato polynomials for the structure sheaf $\\mathcal{O}_X$ and a hypersurface $(f=0)$ in $X$, where $X$ is a regular variety over an $F$-finite field of positive characteristic (see arxiv:0711.3794). He shows that the suitably interpreted zeros of his Bernstein-Sato polynomials correspond to the jumping numbers of the test ideal filtration $\\tau(X,f^t)$. In the present paper we generalize Musta\\c{t}\\u{a}'s construction replacing $\\mathcal{O}_X$ by an arbitrary $F$-regular Cartier module $M$ on $X$ and ","authors_text":"Axel St\\\"abler, Manuel Blickle","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-02-06T12:08:32Z","title":"Bernstein-Sato polynomials and test modules in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1333","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":"sha256:40448e75054ab7ba52dc91461372b008b50099255e0f95d7da8189ab399e24b3","target":"record","created_at":"2026-05-18T02:18:22Z","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":"d8558e194df11d33ac6be084ad20a2d3409f10c843f071145c89015da85efa4f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-02-06T12:08:32Z","title_canon_sha256":"0b9d241832fad482f531cf36773599ff15813ba2e88c410db36fb564735f06fb"},"schema_version":"1.0","source":{"id":"1402.1333","kind":"arxiv","version":2}},"canonical_sha256":"802deccf6b42a79c85df16d12361d0af891fcd74cfeed3620314deecee377cb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"802deccf6b42a79c85df16d12361d0af891fcd74cfeed3620314deecee377cb6","first_computed_at":"2026-05-18T02:18:22.160645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:22.160645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YTHv5urY/DE82fhpc53yQb/1z2+MnlYoUgCem0hV3JuXXVWU3MpUDeKunI/S3GX9MqPeT/F2CrNz79hgrNJ0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:22.161294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.1333","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40448e75054ab7ba52dc91461372b008b50099255e0f95d7da8189ab399e24b3","sha256:5d3c1a79d57fb58860767c33987049df8b34ca18d8439860cbb0b61076cc0de2"],"state_sha256":"893522ae7fad70fa9246c2542b7e0022f5fe828e2e45677554fdcc4fb3b8a6bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wv0Zqvtzfx4Sxq6i/ICnbMnfohjdeGk0UrWNnX83r0JADF/+46vRxrO/20VwEgd5SWy4FjNdzS0Jk9dWQ3NsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:22:25.406830Z","bundle_sha256":"f9dd94217d268ae3e160db4b267b16187219ee1a02696d13c3c9944c20565638"}}