{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SQL477JI2WMIG5AKA5NWUNRPC4","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":"7a7e276f24bd730902d34a88c597a14277e7ba30e02d37cfa49fa8f79ed68a5f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-10-13T15:39:31Z","title_canon_sha256":"c262e48cc24cd40b735d7049b392ed5221791bac0e67103af777649ff16a7c6a"},"schema_version":"1.0","source":{"id":"2510.11540","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.11540","created_at":"2026-06-11T01:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"2510.11540v4","created_at":"2026-06-11T01:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.11540","created_at":"2026-06-11T01:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"SQL477JI2WMI","created_at":"2026-06-11T01:09:20Z"},{"alias_kind":"pith_short_16","alias_value":"SQL477JI2WMIG5AK","created_at":"2026-06-11T01:09:20Z"},{"alias_kind":"pith_short_8","alias_value":"SQL477JI","created_at":"2026-06-11T01:09:20Z"}],"graph_snapshots":[{"event_id":"sha256:6159ab212b8d64b189fcf1ceb230f81b17da0ed1ed0112592fffb7fbad3d8141","target":"graph","created_at":"2026-06-11T01:09:20Z","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/2510.11540/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Suppose $J = (f_1, \\dots, f_n)$ is an $n$-generated ideal in any ring $R$. We prove a general Brian\\c{c}on-Skoda-type containment relating the integral closure $\\overline{J^{n+k-1}}$ with ordinary powers $J^k$. We prove that our result implies the full Brian\\c{c}on-Skoda containment $\\overline{J^{n+k-1}} \\subseteq J^k$ for pseudo-rational singularities (for instance regular rings), and even for the weaker condition of birational derived splinters. Our methods also yield the containment $\\overline{J^{n+k}} \\subseteq J^k$ for Du Bois singularities and even for a characteristic-free generalizatio","authors_text":"Karl Schwede, Linquan Ma, Peter M. McDonald, Rebecca R.G.","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-10-13T15:39:31Z","title":"The Brian\\c{c}on-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.11540","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:aa9a6ed9956cdb3cdf0371a44d3c0b7bbc9cf6f50be89e45a0559d1134b5ce01","target":"record","created_at":"2026-06-11T01:09:20Z","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":"7a7e276f24bd730902d34a88c597a14277e7ba30e02d37cfa49fa8f79ed68a5f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-10-13T15:39:31Z","title_canon_sha256":"c262e48cc24cd40b735d7049b392ed5221791bac0e67103af777649ff16a7c6a"},"schema_version":"1.0","source":{"id":"2510.11540","kind":"arxiv","version":4}},"canonical_sha256":"9417cffd28d59883740a075b6a362f172ccbc5cc15c68bbbadd50bdae097626f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9417cffd28d59883740a075b6a362f172ccbc5cc15c68bbbadd50bdae097626f","first_computed_at":"2026-06-11T01:09:20.088530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:09:20.088530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0pH8B7ABBGx5jPl4MNVaThCZgMxte2bC2syaCU+5JzowcH10BogE+WUNopjNVqjDNwZqajf9vu0UqUv3Xay4BA==","signature_status":"signed_v1","signed_at":"2026-06-11T01:09:20.089640Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.11540","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa9a6ed9956cdb3cdf0371a44d3c0b7bbc9cf6f50be89e45a0559d1134b5ce01","sha256:6159ab212b8d64b189fcf1ceb230f81b17da0ed1ed0112592fffb7fbad3d8141"],"state_sha256":"713ccd10295633d253c2873aefcbc44a5ebb98179d75bc17b76ffe110e7310ff"}