{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:F2WSFUWC4ILVESBBWBD64AAL6L","short_pith_number":"pith:F2WSFUWC","canonical_record":{"source":{"id":"2504.02966","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-04-03T18:35:24Z","cross_cats_sorted":[],"title_canon_sha256":"4846c6cb541d81c131f2feefad84bf48da4b1997dba6abdc1d20fdac6773c277","abstract_canon_sha256":"7194028b7164a539e94215b39814cf236eb626463dec802b63a63aa63d50f1cd"},"schema_version":"1.0"},"canonical_sha256":"2ead22d2c2e217524821b047ee000bf2f4aa3aa54d9de4fc7c3abf2022436c07","source":{"kind":"arxiv","id":"2504.02966","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.02966","created_at":"2026-07-05T11:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"2504.02966v2","created_at":"2026-07-05T11:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.02966","created_at":"2026-07-05T11:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"F2WSFUWC4ILV","created_at":"2026-07-05T11:07:23Z"},{"alias_kind":"pith_short_16","alias_value":"F2WSFUWC4ILVESBB","created_at":"2026-07-05T11:07:23Z"},{"alias_kind":"pith_short_8","alias_value":"F2WSFUWC","created_at":"2026-07-05T11:07:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:F2WSFUWC4ILVESBBWBD64AAL6L","target":"record","payload":{"canonical_record":{"source":{"id":"2504.02966","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-04-03T18:35:24Z","cross_cats_sorted":[],"title_canon_sha256":"4846c6cb541d81c131f2feefad84bf48da4b1997dba6abdc1d20fdac6773c277","abstract_canon_sha256":"7194028b7164a539e94215b39814cf236eb626463dec802b63a63aa63d50f1cd"},"schema_version":"1.0"},"canonical_sha256":"2ead22d2c2e217524821b047ee000bf2f4aa3aa54d9de4fc7c3abf2022436c07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:07:23.226152Z","signature_b64":"Od1rEJUfaktRdcZnhVms9vTK7OlXYNEsLlhLaXNNPy3ccPpdvV3KFVfjJ8QmEBSAdvrW4sPLX8MwB8OMPgt8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ead22d2c2e217524821b047ee000bf2f4aa3aa54d9de4fc7c3abf2022436c07","last_reissued_at":"2026-07-05T11:07:23.225669Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:07:23.225669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.02966","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":"2026-07-05T11:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1y0L6M4fH3MRIolr5Kuc/xmh0hXoSDEsyZOYE3bZXn0kvv467pj1DhgwpHjtoil+Y8m84FNmAU4t68wRZb+8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T08:08:15.286229Z"},"content_sha256":"0c949323a89e862e4f4433f36baebdbeff6b7bf465f8a0b19b993f31101b5de6","schema_version":"1.0","event_id":"sha256:0c949323a89e862e4f4433f36baebdbeff6b7bf465f8a0b19b993f31101b5de6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:F2WSFUWC4ILVESBBWBD64AAL6L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On deformation of perfectoid purity in Gorenstein domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Austyn Simpson, Benjamin Baily, Jack Westbrook, Karina Dovgodko","submitted_at":"2025-04-03T18:35:24Z","abstract_excerpt":"If $(R,\\mathfrak{m})$ is a complete local ring of mixed characteristic $(0,p)$ and $R/pR$ is an $F$-pure Gorenstein domain, we find a sufficient condition for $R$ to be perfectoid pure. This condition is related to the Cohen-Macaulayness of the absolute integral closures of Gorenstein local domains of mixed characteristic which are not necessarily excellent. Along the way, we show that the problem of lifting $F$-purity of $R/pR$ to perfectoid purity of $R$ is equivalent to a similar deformation problem for the splinter property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.02966","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/2504.02966/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":"2026-07-05T11:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1R/4jHVZFy0H7xAO0NDmdUH5R6hxn9Z1ww2FF4t4zr4Upd/duPodg00/ke2gjUtGP75dae9gSSAYsBZZ9/TKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T08:08:15.286844Z"},"content_sha256":"7856175bd0a59e409ae9c07c62bd8a5ef9fb5887a2622d53eaf2d70c1c9e32c2","schema_version":"1.0","event_id":"sha256:7856175bd0a59e409ae9c07c62bd8a5ef9fb5887a2622d53eaf2d70c1c9e32c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L/bundle.json","state_url":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F2WSFUWC4ILVESBBWBD64AAL6L/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":"2026-08-20T08:08:15Z","links":{"resolver":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L","bundle":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L/bundle.json","state":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F2WSFUWC4ILVESBBWBD64AAL6L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:F2WSFUWC4ILVESBBWBD64AAL6L","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":"7194028b7164a539e94215b39814cf236eb626463dec802b63a63aa63d50f1cd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-04-03T18:35:24Z","title_canon_sha256":"4846c6cb541d81c131f2feefad84bf48da4b1997dba6abdc1d20fdac6773c277"},"schema_version":"1.0","source":{"id":"2504.02966","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.02966","created_at":"2026-07-05T11:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"2504.02966v2","created_at":"2026-07-05T11:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.02966","created_at":"2026-07-05T11:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"F2WSFUWC4ILV","created_at":"2026-07-05T11:07:23Z"},{"alias_kind":"pith_short_16","alias_value":"F2WSFUWC4ILVESBB","created_at":"2026-07-05T11:07:23Z"},{"alias_kind":"pith_short_8","alias_value":"F2WSFUWC","created_at":"2026-07-05T11:07:23Z"}],"graph_snapshots":[{"event_id":"sha256:7856175bd0a59e409ae9c07c62bd8a5ef9fb5887a2622d53eaf2d70c1c9e32c2","target":"graph","created_at":"2026-07-05T11:07:23Z","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/2504.02966/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"If $(R,\\mathfrak{m})$ is a complete local ring of mixed characteristic $(0,p)$ and $R/pR$ is an $F$-pure Gorenstein domain, we find a sufficient condition for $R$ to be perfectoid pure. This condition is related to the Cohen-Macaulayness of the absolute integral closures of Gorenstein local domains of mixed characteristic which are not necessarily excellent. Along the way, we show that the problem of lifting $F$-purity of $R/pR$ to perfectoid purity of $R$ is equivalent to a similar deformation problem for the splinter property.","authors_text":"Austyn Simpson, Benjamin Baily, Jack Westbrook, Karina Dovgodko","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-04-03T18:35:24Z","title":"On deformation of perfectoid purity in Gorenstein domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.02966","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":"sha256:0c949323a89e862e4f4433f36baebdbeff6b7bf465f8a0b19b993f31101b5de6","target":"record","created_at":"2026-07-05T11:07:23Z","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":"7194028b7164a539e94215b39814cf236eb626463dec802b63a63aa63d50f1cd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-04-03T18:35:24Z","title_canon_sha256":"4846c6cb541d81c131f2feefad84bf48da4b1997dba6abdc1d20fdac6773c277"},"schema_version":"1.0","source":{"id":"2504.02966","kind":"arxiv","version":2}},"canonical_sha256":"2ead22d2c2e217524821b047ee000bf2f4aa3aa54d9de4fc7c3abf2022436c07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ead22d2c2e217524821b047ee000bf2f4aa3aa54d9de4fc7c3abf2022436c07","first_computed_at":"2026-07-05T11:07:23.225669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:07:23.225669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Od1rEJUfaktRdcZnhVms9vTK7OlXYNEsLlhLaXNNPy3ccPpdvV3KFVfjJ8QmEBSAdvrW4sPLX8MwB8OMPgt8Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:07:23.226152Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.02966","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c949323a89e862e4f4433f36baebdbeff6b7bf465f8a0b19b993f31101b5de6","sha256:7856175bd0a59e409ae9c07c62bd8a5ef9fb5887a2622d53eaf2d70c1c9e32c2"],"state_sha256":"f186edeb165ad88fd6abf9968f70fa7cbcd33ce39e5f4318b7cc3880ed25602e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cVXPiMzAlx/PomsO8r/arTecsiCAOA/wTrVgKyV4PQ2suVFw0VEe2d/GCf4u+XHwnNnK9IxNrb8nM+3v1GU9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T08:08:15.291673Z","bundle_sha256":"efea0099e69b466c4c6d12302add83aff94ed5974362ce41723760bcf17166a4"}}