{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6KQVLO4NM5BKPNTWHOJTURHIPH","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":"b1331c51b01553551af5fa80dd0691dda75633d650ad2a6040ceb2a1ca335f6a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-02-07T01:37:18Z","title_canon_sha256":"e51dcd4cb063176fd8de37fd31953dcd5605b89d12b88204b42df37936599217"},"schema_version":"1.0","source":{"id":"2402.04512","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.04512","created_at":"2026-07-05T09:28:10Z"},{"alias_kind":"arxiv_version","alias_value":"2402.04512v4","created_at":"2026-07-05T09:28:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.04512","created_at":"2026-07-05T09:28:10Z"},{"alias_kind":"pith_short_12","alias_value":"6KQVLO4NM5BK","created_at":"2026-07-05T09:28:10Z"},{"alias_kind":"pith_short_16","alias_value":"6KQVLO4NM5BKPNTW","created_at":"2026-07-05T09:28:10Z"},{"alias_kind":"pith_short_8","alias_value":"6KQVLO4N","created_at":"2026-07-05T09:28:10Z"}],"graph_snapshots":[{"event_id":"sha256:1bf55e32ef5c39e512a2ecee5d9df8959e9bfa5696a3c448f1fff5e28df9e5e7","target":"graph","created_at":"2026-07-05T09:28:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.04512/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that if $f\\in \\mathcal{O}_X(X)$ and $g\\in \\mathcal{O}_Y(Y)$ are nonzero regular functions on smooth complex algebraic varieties $X$ and $Y$, then the Bernstein-Sato polynomial of the product function $fg \\in \\mathcal{O}_{X\\times Y}(X \\times Y)$ is given by $b_{fg}(s)=b_f(s)b_g(s)$, answering a question of Budur and Popa.","authors_text":"Jonghyun Lee","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-02-07T01:37:18Z","title":"Multiplicative Thom-Sebastiani for Bernstein-Sato polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.04512","kind":"arxiv","version":4},"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":"sha256:5d379b615e7202dbd648943d901f85e9524d831800235901b10b9296c3825803","target":"record","created_at":"2026-07-05T09:28:10Z","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":"b1331c51b01553551af5fa80dd0691dda75633d650ad2a6040ceb2a1ca335f6a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-02-07T01:37:18Z","title_canon_sha256":"e51dcd4cb063176fd8de37fd31953dcd5605b89d12b88204b42df37936599217"},"schema_version":"1.0","source":{"id":"2402.04512","kind":"arxiv","version":4}},"canonical_sha256":"f2a155bb8d6742a7b6763b933a44e879eca7d49f5fdacbe12c2c8c5703ddffe6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2a155bb8d6742a7b6763b933a44e879eca7d49f5fdacbe12c2c8c5703ddffe6","first_computed_at":"2026-07-05T09:28:10.433153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:28:10.433153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pIXicaWgsMnwi/ADHrnBhon8XL3/LwLvDeMxBdJsldDCWtJkvNw8kqCm6SDqfYtSirUNO2nW8tm4g1mLmGnuBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:28:10.433650Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.04512","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d379b615e7202dbd648943d901f85e9524d831800235901b10b9296c3825803","sha256:1bf55e32ef5c39e512a2ecee5d9df8959e9bfa5696a3c448f1fff5e28df9e5e7"],"state_sha256":"8afc405d806735118d52423e030c510125c4b09985136813a0f692e99bd8d997"}