{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GHPK3XPTPSDV2VMH4MMDLT2LHM","short_pith_number":"pith:GHPK3XPT","canonical_record":{"source":{"id":"2605.27337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-05-26T17:44:35Z","cross_cats_sorted":[],"title_canon_sha256":"afc5a8f201ab9624e40857108a38f58cf060b4a5fc0a187605b7203537d5b3f0","abstract_canon_sha256":"3aae5079c3c147aa9e17b9f344e3ad8ced62acc3657cef001c91f6126d5f9351"},"schema_version":"1.0"},"canonical_sha256":"31deadddf37c875d5587e31835cf4b3b047674f23ea1dd8f8d33c90621b0a44d","source":{"kind":"arxiv","id":"2605.27337","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27337","created_at":"2026-05-27T02:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27337v1","created_at":"2026-05-27T02:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27337","created_at":"2026-05-27T02:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"GHPK3XPTPSDV","created_at":"2026-05-27T02:06:18Z"},{"alias_kind":"pith_short_16","alias_value":"GHPK3XPTPSDV2VMH","created_at":"2026-05-27T02:06:18Z"},{"alias_kind":"pith_short_8","alias_value":"GHPK3XPT","created_at":"2026-05-27T02:06:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GHPK3XPTPSDV2VMH4MMDLT2LHM","target":"record","payload":{"canonical_record":{"source":{"id":"2605.27337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-05-26T17:44:35Z","cross_cats_sorted":[],"title_canon_sha256":"afc5a8f201ab9624e40857108a38f58cf060b4a5fc0a187605b7203537d5b3f0","abstract_canon_sha256":"3aae5079c3c147aa9e17b9f344e3ad8ced62acc3657cef001c91f6126d5f9351"},"schema_version":"1.0"},"canonical_sha256":"31deadddf37c875d5587e31835cf4b3b047674f23ea1dd8f8d33c90621b0a44d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T02:06:18.723277Z","signature_b64":"A/CTfB811uAihSSKcIE2OJreVJ0gGb9O9+rObjMwYe3b7DARkaDxY4MMC59q6rn9RW8c2rL/Ynyza9s3vvn5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31deadddf37c875d5587e31835cf4b3b047674f23ea1dd8f8d33c90621b0a44d","last_reissued_at":"2026-05-27T02:06:18.722531Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T02:06:18.722531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.27337","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-27T02:06:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xnaTbKIo/YtMld0cUK2gFemeyn6s0BCCu3lcPxlxWqk5Le2/c9g73zRboB7YmMq51UhN8O07xte2IbZo/oQ4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:12:21.436659Z"},"content_sha256":"92ec952177323d655bda3400858fc82b0a2f2adda41776fddc4f58f329dedf7c","schema_version":"1.0","event_id":"sha256:92ec952177323d655bda3400858fc82b0a2f2adda41776fddc4f58f329dedf7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GHPK3XPTPSDV2VMH4MMDLT2LHM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regular rings and perfectoid towers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kazuki Hayashi","submitted_at":"2026-05-26T17:44:35Z","abstract_excerpt":"We prove a mixed-characteristic analogue of Kunz's theorem in terms of perfectoid towers: a Noetherian local ring of residue characteristic $p$ is regular if and only if it admits a flat map to a Noetherian ring that extends to a perfectoid tower. This result is deduced from another mixed-characteristic analogue due to O. Gabber and J. Lurie. We also characterize regularity for perfectoid towers via vanishing of single higher $\\mathrm{Tor}$-module of the residue field with a perfectoid algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27337","kind":"arxiv","version":1},"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/2605.27337/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":"2026-05-27T02:06:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SIQ+ENa/kZEOXxYgl+ACkicfALr3letggnNQQr7azSgGO4VAUMbU4fgPL4i4m/cPKfDeMkF9OKJqOTCFp+3NDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:12:21.437710Z"},"content_sha256":"250d955d913150d16cb1432e275794a0969717e89aa27f7599744078767277d5","schema_version":"1.0","event_id":"sha256:250d955d913150d16cb1432e275794a0969717e89aa27f7599744078767277d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHPK3XPTPSDV2VMH4MMDLT2LHM/bundle.json","state_url":"https://pith.science/pith/GHPK3XPTPSDV2VMH4MMDLT2LHM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHPK3XPTPSDV2VMH4MMDLT2LHM/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":"2026-08-08T16:12:21Z","links":{"resolver":"https://pith.science/pith/GHPK3XPTPSDV2VMH4MMDLT2LHM","bundle":"https://pith.science/pith/GHPK3XPTPSDV2VMH4MMDLT2LHM/bundle.json","state":"https://pith.science/pith/GHPK3XPTPSDV2VMH4MMDLT2LHM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHPK3XPTPSDV2VMH4MMDLT2LHM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GHPK3XPTPSDV2VMH4MMDLT2LHM","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":"3aae5079c3c147aa9e17b9f344e3ad8ced62acc3657cef001c91f6126d5f9351","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-05-26T17:44:35Z","title_canon_sha256":"afc5a8f201ab9624e40857108a38f58cf060b4a5fc0a187605b7203537d5b3f0"},"schema_version":"1.0","source":{"id":"2605.27337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27337","created_at":"2026-05-27T02:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27337v1","created_at":"2026-05-27T02:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27337","created_at":"2026-05-27T02:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"GHPK3XPTPSDV","created_at":"2026-05-27T02:06:18Z"},{"alias_kind":"pith_short_16","alias_value":"GHPK3XPTPSDV2VMH","created_at":"2026-05-27T02:06:18Z"},{"alias_kind":"pith_short_8","alias_value":"GHPK3XPT","created_at":"2026-05-27T02:06:18Z"}],"graph_snapshots":[{"event_id":"sha256:250d955d913150d16cb1432e275794a0969717e89aa27f7599744078767277d5","target":"graph","created_at":"2026-05-27T02:06:18Z","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/2605.27337/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a mixed-characteristic analogue of Kunz's theorem in terms of perfectoid towers: a Noetherian local ring of residue characteristic $p$ is regular if and only if it admits a flat map to a Noetherian ring that extends to a perfectoid tower. This result is deduced from another mixed-characteristic analogue due to O. Gabber and J. Lurie. We also characterize regularity for perfectoid towers via vanishing of single higher $\\mathrm{Tor}$-module of the residue field with a perfectoid algebra.","authors_text":"Kazuki Hayashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-05-26T17:44:35Z","title":"Regular rings and perfectoid towers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27337","kind":"arxiv","version":1},"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":"sha256:92ec952177323d655bda3400858fc82b0a2f2adda41776fddc4f58f329dedf7c","target":"record","created_at":"2026-05-27T02:06:18Z","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":"3aae5079c3c147aa9e17b9f344e3ad8ced62acc3657cef001c91f6126d5f9351","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-05-26T17:44:35Z","title_canon_sha256":"afc5a8f201ab9624e40857108a38f58cf060b4a5fc0a187605b7203537d5b3f0"},"schema_version":"1.0","source":{"id":"2605.27337","kind":"arxiv","version":1}},"canonical_sha256":"31deadddf37c875d5587e31835cf4b3b047674f23ea1dd8f8d33c90621b0a44d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31deadddf37c875d5587e31835cf4b3b047674f23ea1dd8f8d33c90621b0a44d","first_computed_at":"2026-05-27T02:06:18.722531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T02:06:18.722531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A/CTfB811uAihSSKcIE2OJreVJ0gGb9O9+rObjMwYe3b7DARkaDxY4MMC59q6rn9RW8c2rL/Ynyza9s3vvn5Aw==","signature_status":"signed_v1","signed_at":"2026-05-27T02:06:18.723277Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92ec952177323d655bda3400858fc82b0a2f2adda41776fddc4f58f329dedf7c","sha256:250d955d913150d16cb1432e275794a0969717e89aa27f7599744078767277d5"],"state_sha256":"78766bee91d95264fb93666be57c5115ee47f9015cace34ee4560b57b278491a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbRZyZ9CfDiCbhOxy4C17DFiQo/s7UkrFOAI7DVLlhy//1Eok6LQvAx4lKsTMUy9DRXEYGDIG1Pqk+gthevBBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T16:12:21.448656Z","bundle_sha256":"2a68ce2329ca31ffe7c0d37639243477f96f3cc88d8f8afce6c6e0b39ae6d15e"}}