{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FUV5EF2CMEEDF3PS3WKGEEANCJ","short_pith_number":"pith:FUV5EF2C","canonical_record":{"source":{"id":"2406.02433","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-06-04T15:50:58Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bb35dcbbf622005d08c4b5247668c58b18d4711acac8fe8615c1ac31dcf1dfd7","abstract_canon_sha256":"e764f92f3e6f07995f5a4f9249fa6c03430a1dfeedc07719709d2e9156171c74"},"schema_version":"1.0"},"canonical_sha256":"2d2bd21742610832edf2dd9462100d125d47cb5d4dd98563b4cdbf587427b2c8","source":{"kind":"arxiv","id":"2406.02433","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.02433","created_at":"2026-07-05T09:02:59Z"},{"alias_kind":"arxiv_version","alias_value":"2406.02433v2","created_at":"2026-07-05T09:02:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.02433","created_at":"2026-07-05T09:02:59Z"},{"alias_kind":"pith_short_12","alias_value":"FUV5EF2CMEED","created_at":"2026-07-05T09:02:59Z"},{"alias_kind":"pith_short_16","alias_value":"FUV5EF2CMEEDF3PS","created_at":"2026-07-05T09:02:59Z"},{"alias_kind":"pith_short_8","alias_value":"FUV5EF2C","created_at":"2026-07-05T09:02:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FUV5EF2CMEEDF3PS3WKGEEANCJ","target":"record","payload":{"canonical_record":{"source":{"id":"2406.02433","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-06-04T15:50:58Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bb35dcbbf622005d08c4b5247668c58b18d4711acac8fe8615c1ac31dcf1dfd7","abstract_canon_sha256":"e764f92f3e6f07995f5a4f9249fa6c03430a1dfeedc07719709d2e9156171c74"},"schema_version":"1.0"},"canonical_sha256":"2d2bd21742610832edf2dd9462100d125d47cb5d4dd98563b4cdbf587427b2c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:02:59.076140Z","signature_b64":"3GxXkCZTPa1aOsR4qNbkTvf+7cpDw/K4jgcid7uo3KS5TgZ2kenQaJO2ghnZS/Jf5BG0TCCTtEr/3l+HfEb7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d2bd21742610832edf2dd9462100d125d47cb5d4dd98563b4cdbf587427b2c8","last_reissued_at":"2026-07-05T09:02:59.075651Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:02:59.075651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.02433","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":"2026-07-05T09:02:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M3ewxYqbl3R1MTBkKQTkgCohl/XK3Cw2KDydwNuLI+Q78KWG8VBrN/C9s2Q3wK6BU+GVBdM+vBD/rOTRkl2pDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:17:02.177124Z"},"content_sha256":"3c250d8e6cd7a54399ff05303ae25fc5acde929c0a4b069a50f9b238c7c2fe5a","schema_version":"1.0","event_id":"sha256:3c250d8e6cd7a54399ff05303ae25fc5acde929c0a4b069a50f9b238c7c2fe5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FUV5EF2CMEEDF3PS3WKGEEANCJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Brian\\c{c}on-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Karl Schwede, Sandra Rodr\\'iguez-Villalobos","submitted_at":"2024-06-04T15:50:58Z","abstract_excerpt":"We prove that, given a sufficiently functorial assignment from rings to big Cohen-Macaulay algebras $R \\mapsto B$, that the associated big Cohen-Macaulay closure operation on ideals $I \\mapsto I B \\cap R$ necessarily satisfies the Brian\\c{c}on-Skoda type property. The proof combines arguments of Lipman-Teissier, Hochster, Ma, and Hochster-Huneke. Specializing to mixed characteristic, and utilizing a result of Bhatt on absolute integral closures, this recovers a slight strengthening of a result of Heitmann."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.02433","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.02433/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:02:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FHqcOwiqqCtOfZ5NbpXmb8ZdysDM2Mw2LU/Cw2TzQ9rjR5BJ0Al9jsjUtCZA6M+ciO78vHKhVxG/ShzjKdPVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:17:02.177619Z"},"content_sha256":"ba07e45f78aa51adde2b567135be6649ce74786fa60f04616e2a7330c4168970","schema_version":"1.0","event_id":"sha256:ba07e45f78aa51adde2b567135be6649ce74786fa60f04616e2a7330c4168970"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FUV5EF2CMEEDF3PS3WKGEEANCJ/bundle.json","state_url":"https://pith.science/pith/FUV5EF2CMEEDF3PS3WKGEEANCJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FUV5EF2CMEEDF3PS3WKGEEANCJ/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":"2026-08-09T03:17:02Z","links":{"resolver":"https://pith.science/pith/FUV5EF2CMEEDF3PS3WKGEEANCJ","bundle":"https://pith.science/pith/FUV5EF2CMEEDF3PS3WKGEEANCJ/bundle.json","state":"https://pith.science/pith/FUV5EF2CMEEDF3PS3WKGEEANCJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FUV5EF2CMEEDF3PS3WKGEEANCJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FUV5EF2CMEEDF3PS3WKGEEANCJ","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":"e764f92f3e6f07995f5a4f9249fa6c03430a1dfeedc07719709d2e9156171c74","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-06-04T15:50:58Z","title_canon_sha256":"bb35dcbbf622005d08c4b5247668c58b18d4711acac8fe8615c1ac31dcf1dfd7"},"schema_version":"1.0","source":{"id":"2406.02433","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.02433","created_at":"2026-07-05T09:02:59Z"},{"alias_kind":"arxiv_version","alias_value":"2406.02433v2","created_at":"2026-07-05T09:02:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.02433","created_at":"2026-07-05T09:02:59Z"},{"alias_kind":"pith_short_12","alias_value":"FUV5EF2CMEED","created_at":"2026-07-05T09:02:59Z"},{"alias_kind":"pith_short_16","alias_value":"FUV5EF2CMEEDF3PS","created_at":"2026-07-05T09:02:59Z"},{"alias_kind":"pith_short_8","alias_value":"FUV5EF2C","created_at":"2026-07-05T09:02:59Z"}],"graph_snapshots":[{"event_id":"sha256:ba07e45f78aa51adde2b567135be6649ce74786fa60f04616e2a7330c4168970","target":"graph","created_at":"2026-07-05T09:02:59Z","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/2406.02433/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that, given a sufficiently functorial assignment from rings to big Cohen-Macaulay algebras $R \\mapsto B$, that the associated big Cohen-Macaulay closure operation on ideals $I \\mapsto I B \\cap R$ necessarily satisfies the Brian\\c{c}on-Skoda type property. The proof combines arguments of Lipman-Teissier, Hochster, Ma, and Hochster-Huneke. Specializing to mixed characteristic, and utilizing a result of Bhatt on absolute integral closures, this recovers a slight strengthening of a result of Heitmann.","authors_text":"Karl Schwede, Sandra Rodr\\'iguez-Villalobos","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-06-04T15:50:58Z","title":"The Brian\\c{c}on-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.02433","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":"sha256:3c250d8e6cd7a54399ff05303ae25fc5acde929c0a4b069a50f9b238c7c2fe5a","target":"record","created_at":"2026-07-05T09:02:59Z","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":"e764f92f3e6f07995f5a4f9249fa6c03430a1dfeedc07719709d2e9156171c74","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-06-04T15:50:58Z","title_canon_sha256":"bb35dcbbf622005d08c4b5247668c58b18d4711acac8fe8615c1ac31dcf1dfd7"},"schema_version":"1.0","source":{"id":"2406.02433","kind":"arxiv","version":2}},"canonical_sha256":"2d2bd21742610832edf2dd9462100d125d47cb5d4dd98563b4cdbf587427b2c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d2bd21742610832edf2dd9462100d125d47cb5d4dd98563b4cdbf587427b2c8","first_computed_at":"2026-07-05T09:02:59.075651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:02:59.075651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3GxXkCZTPa1aOsR4qNbkTvf+7cpDw/K4jgcid7uo3KS5TgZ2kenQaJO2ghnZS/Jf5BG0TCCTtEr/3l+HfEb7Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:02:59.076140Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.02433","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c250d8e6cd7a54399ff05303ae25fc5acde929c0a4b069a50f9b238c7c2fe5a","sha256:ba07e45f78aa51adde2b567135be6649ce74786fa60f04616e2a7330c4168970"],"state_sha256":"28a01a4c63959e725ee372a52eacea1360619884548b1ff543fea3c18ddbd0dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s//oScINilYF+/4EBIOQZHJIRBTI9bRjHXMbEy2wZ3jM7Em59VN7indPi/lvtQSJmIsOmOoZwoKq1b1LCf/LDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T03:17:02.181733Z","bundle_sha256":"96215d0af0d1b33e0578b6d205a43dfb6334757de942d05b39900474abc7cf01"}}