{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:5FD72R34VX76G4LI5KZ7MM2BY3","short_pith_number":"pith:5FD72R34","canonical_record":{"source":{"id":"2605.27279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-05-26T16:57:46Z","cross_cats_sorted":[],"title_canon_sha256":"71f455d5e0bf9afe4424d53333d0cbe530705b55a0fba31d5f34fac245cd4397","abstract_canon_sha256":"29f0040aecfd220b445d5f94d1a0cc3c6705f3036d1415c0d2b9521d10bec64e"},"schema_version":"1.0"},"canonical_sha256":"e947fd477cadffe37168eab3f63341c6fe3a34b957eca0af34d289eb415c3a2a","source":{"kind":"arxiv","id":"2605.27279","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27279","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27279v1","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27279","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"5FD72R34VX76","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"pith_short_16","alias_value":"5FD72R34VX76G4LI","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"pith_short_8","alias_value":"5FD72R34","created_at":"2026-05-27T02:06:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:5FD72R34VX76G4LI5KZ7MM2BY3","target":"record","payload":{"canonical_record":{"source":{"id":"2605.27279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-05-26T16:57:46Z","cross_cats_sorted":[],"title_canon_sha256":"71f455d5e0bf9afe4424d53333d0cbe530705b55a0fba31d5f34fac245cd4397","abstract_canon_sha256":"29f0040aecfd220b445d5f94d1a0cc3c6705f3036d1415c0d2b9521d10bec64e"},"schema_version":"1.0"},"canonical_sha256":"e947fd477cadffe37168eab3f63341c6fe3a34b957eca0af34d289eb415c3a2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T02:06:15.055308Z","signature_b64":"lLgEcvKp8V3pn3WGDfH90zocU3QEsrggrIfaqHOrqGqHkcByf8bbl6HREW8asqll4Qq7yUYUDDsqPEJDq85eCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e947fd477cadffe37168eab3f63341c6fe3a34b957eca0af34d289eb415c3a2a","last_reissued_at":"2026-05-27T02:06:15.054490Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T02:06:15.054490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.27279","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":"2026-05-27T02:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"meTVLj2+giM/MYTthl3xsqKj6yEf62SNFTdEDzdWfGEKapkXNvMBO1Eisfr+O5Hyrd0r+CBTgZ3dwg+Iu1y2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:39:24.076652Z"},"content_sha256":"1f62cf3d3293830d892f73bb6ed65dfa5b8b98ebc8c2963fc3c7fef08b1ab564","schema_version":"1.0","event_id":"sha256:1f62cf3d3293830d892f73bb6ed65dfa5b8b98ebc8c2963fc3c7fef08b1ab564"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:5FD72R34VX76G4LI5KZ7MM2BY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A characterization of perfectoid towers in terms of conormal cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kazuki Hayashi","submitted_at":"2026-05-26T16:57:46Z","abstract_excerpt":"We characterize perfectoid towers in terms of conormal cones rather than torsion parts. This result is deduced from a refined study of the relationship between torsion with respect to a principal ideal and the associated conormal cone, building on the work of O. Gabber and L. Ramero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27279","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/2605.27279/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":"2026-05-27T02:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJb1rmKQZMCin941N43uQb9mV0Qcb/LXDfOixn3rOFgmGpAS2uSXS5zViBUq7y2RvURihSiLrwvOleGqbtpjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:39:24.077163Z"},"content_sha256":"03248ffb2f17aeaae62d28eadd73d7656b5a22bc68a93a375134a9f2ecb34c82","schema_version":"1.0","event_id":"sha256:03248ffb2f17aeaae62d28eadd73d7656b5a22bc68a93a375134a9f2ecb34c82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5FD72R34VX76G4LI5KZ7MM2BY3/bundle.json","state_url":"https://pith.science/pith/5FD72R34VX76G4LI5KZ7MM2BY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5FD72R34VX76G4LI5KZ7MM2BY3/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":"2026-08-08T14:39:24Z","links":{"resolver":"https://pith.science/pith/5FD72R34VX76G4LI5KZ7MM2BY3","bundle":"https://pith.science/pith/5FD72R34VX76G4LI5KZ7MM2BY3/bundle.json","state":"https://pith.science/pith/5FD72R34VX76G4LI5KZ7MM2BY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5FD72R34VX76G4LI5KZ7MM2BY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5FD72R34VX76G4LI5KZ7MM2BY3","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":"29f0040aecfd220b445d5f94d1a0cc3c6705f3036d1415c0d2b9521d10bec64e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-05-26T16:57:46Z","title_canon_sha256":"71f455d5e0bf9afe4424d53333d0cbe530705b55a0fba31d5f34fac245cd4397"},"schema_version":"1.0","source":{"id":"2605.27279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27279","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27279v1","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27279","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"5FD72R34VX76","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"pith_short_16","alias_value":"5FD72R34VX76G4LI","created_at":"2026-05-27T02:06:15Z"},{"alias_kind":"pith_short_8","alias_value":"5FD72R34","created_at":"2026-05-27T02:06:15Z"}],"graph_snapshots":[{"event_id":"sha256:03248ffb2f17aeaae62d28eadd73d7656b5a22bc68a93a375134a9f2ecb34c82","target":"graph","created_at":"2026-05-27T02:06:15Z","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/2605.27279/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We characterize perfectoid towers in terms of conormal cones rather than torsion parts. This result is deduced from a refined study of the relationship between torsion with respect to a principal ideal and the associated conormal cone, building on the work of O. Gabber and L. Ramero.","authors_text":"Kazuki Hayashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-05-26T16:57:46Z","title":"A characterization of perfectoid towers in terms of conormal cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27279","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":"sha256:1f62cf3d3293830d892f73bb6ed65dfa5b8b98ebc8c2963fc3c7fef08b1ab564","target":"record","created_at":"2026-05-27T02:06:15Z","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":"29f0040aecfd220b445d5f94d1a0cc3c6705f3036d1415c0d2b9521d10bec64e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-05-26T16:57:46Z","title_canon_sha256":"71f455d5e0bf9afe4424d53333d0cbe530705b55a0fba31d5f34fac245cd4397"},"schema_version":"1.0","source":{"id":"2605.27279","kind":"arxiv","version":1}},"canonical_sha256":"e947fd477cadffe37168eab3f63341c6fe3a34b957eca0af34d289eb415c3a2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e947fd477cadffe37168eab3f63341c6fe3a34b957eca0af34d289eb415c3a2a","first_computed_at":"2026-05-27T02:06:15.054490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T02:06:15.054490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lLgEcvKp8V3pn3WGDfH90zocU3QEsrggrIfaqHOrqGqHkcByf8bbl6HREW8asqll4Qq7yUYUDDsqPEJDq85eCQ==","signature_status":"signed_v1","signed_at":"2026-05-27T02:06:15.055308Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f62cf3d3293830d892f73bb6ed65dfa5b8b98ebc8c2963fc3c7fef08b1ab564","sha256:03248ffb2f17aeaae62d28eadd73d7656b5a22bc68a93a375134a9f2ecb34c82"],"state_sha256":"5a70a145969912e1ee0fd8223da24094276a6694256e84e853c82b0966a856b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4olTgd5qrB5GlyaIFTgoIs8X6B6NaO87nwOpRsr7Xu0ZmAzl0DNXcPCQKtH5f3oAiAAegrkVpZZCHpB3G2OdDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T14:39:24.081071Z","bundle_sha256":"ce35f72390c4f9f07d3125d9e51477b19adc7e29668ac519cdc2b1fb40d350e7"}}