{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OYDG4J3LRGNWKZOH4IXNGGTVUV","short_pith_number":"pith:OYDG4J3L","canonical_record":{"source":{"id":"1309.0574","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-03T02:25:53Z","cross_cats_sorted":[],"title_canon_sha256":"8c048f885f4e110da2a92c994b9ed573248e3906e03f16e69fb49d318b328c59","abstract_canon_sha256":"5f491d5087ee8db9c375f7e338eae00cd8b1141c7d70c5ab61915372bd28a267"},"schema_version":"1.0"},"canonical_sha256":"76066e276b899b6565c7e22ed31a75a5432d135e03b60fb3ac6af7883ea8a09f","source":{"kind":"arxiv","id":"1309.0574","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0574","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0574v5","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0574","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"OYDG4J3LRGNW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OYDG4J3LRGNWKZOH","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OYDG4J3L","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OYDG4J3LRGNWKZOH4IXNGGTVUV","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0574","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-03T02:25:53Z","cross_cats_sorted":[],"title_canon_sha256":"8c048f885f4e110da2a92c994b9ed573248e3906e03f16e69fb49d318b328c59","abstract_canon_sha256":"5f491d5087ee8db9c375f7e338eae00cd8b1141c7d70c5ab61915372bd28a267"},"schema_version":"1.0"},"canonical_sha256":"76066e276b899b6565c7e22ed31a75a5432d135e03b60fb3ac6af7883ea8a09f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:05.292628Z","signature_b64":"nC0QEGWuHptvTnBIjvvNaio6G73qrVLbpdQPhzoVVKjp26GT/kioVxbisr06KO3diMp1gUlK872yg3kr+qLMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76066e276b899b6565c7e22ed31a75a5432d135e03b60fb3ac6af7883ea8a09f","last_reissued_at":"2026-05-18T01:35:05.291966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:05.291966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0574","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLcYhfgD4TE4PM9njUfwJLV35pK4HsoYBxeRJf9Xg3/lUNoC6Zcpp2Bvr7synMYqwK1lEgxwlB7IbiY6FrZJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:32:15.982187Z"},"content_sha256":"beab8356d0aeb98f828ce5f6fcc4173fd0ba179a46a1af12a25ca5df198fdbd1","schema_version":"1.0","event_id":"sha256:beab8356d0aeb98f828ce5f6fcc4173fd0ba179a46a1af12a25ca5df198fdbd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OYDG4J3LRGNWKZOH4IXNGGTVUV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reified valuations and adic spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kiran S. Kedlaya","submitted_at":"2013-09-03T02:25:53Z","abstract_excerpt":"We revisit Huber's theory of continuous valuations, which give rise to the adic spectra used in his theory of adic spaces. We instead consider valuations which have been reified, i.e., whose value groups have been forced to contain the real numbers. This yields reified adic spectra which provide a framework for an analogue of Huber's theory compatible with Berkovich's construction of nonarchimedean analytic spaces. As an example, we extend the theory of perfectoid spaces to this setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0574","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Owg/frIi1zOEBOTAFsDp7Sswkoktp6ZIm1Aq2w8vJbFjR8pVQPLrOI4q7IqgWFG1C7/U9B3ItL2jZOXwrCsJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:32:15.982549Z"},"content_sha256":"b0cf73b2a2eb47dc0991ca9540de9d6bab99379a08885e31a31ef23da3512388","schema_version":"1.0","event_id":"sha256:b0cf73b2a2eb47dc0991ca9540de9d6bab99379a08885e31a31ef23da3512388"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OYDG4J3LRGNWKZOH4IXNGGTVUV/bundle.json","state_url":"https://pith.science/pith/OYDG4J3LRGNWKZOH4IXNGGTVUV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OYDG4J3LRGNWKZOH4IXNGGTVUV/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":"2026-06-21T02:32:15Z","links":{"resolver":"https://pith.science/pith/OYDG4J3LRGNWKZOH4IXNGGTVUV","bundle":"https://pith.science/pith/OYDG4J3LRGNWKZOH4IXNGGTVUV/bundle.json","state":"https://pith.science/pith/OYDG4J3LRGNWKZOH4IXNGGTVUV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OYDG4J3LRGNWKZOH4IXNGGTVUV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OYDG4J3LRGNWKZOH4IXNGGTVUV","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":"5f491d5087ee8db9c375f7e338eae00cd8b1141c7d70c5ab61915372bd28a267","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-03T02:25:53Z","title_canon_sha256":"8c048f885f4e110da2a92c994b9ed573248e3906e03f16e69fb49d318b328c59"},"schema_version":"1.0","source":{"id":"1309.0574","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0574","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0574v5","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0574","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"OYDG4J3LRGNW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OYDG4J3LRGNWKZOH","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OYDG4J3L","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:b0cf73b2a2eb47dc0991ca9540de9d6bab99379a08885e31a31ef23da3512388","target":"graph","created_at":"2026-05-18T01:35:05Z","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"},"paper":{"abstract_excerpt":"We revisit Huber's theory of continuous valuations, which give rise to the adic spectra used in his theory of adic spaces. We instead consider valuations which have been reified, i.e., whose value groups have been forced to contain the real numbers. This yields reified adic spectra which provide a framework for an analogue of Huber's theory compatible with Berkovich's construction of nonarchimedean analytic spaces. As an example, we extend the theory of perfectoid spaces to this setting.","authors_text":"Kiran S. Kedlaya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-03T02:25:53Z","title":"Reified valuations and adic spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0574","kind":"arxiv","version":5},"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:beab8356d0aeb98f828ce5f6fcc4173fd0ba179a46a1af12a25ca5df198fdbd1","target":"record","created_at":"2026-05-18T01:35:05Z","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":"5f491d5087ee8db9c375f7e338eae00cd8b1141c7d70c5ab61915372bd28a267","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-03T02:25:53Z","title_canon_sha256":"8c048f885f4e110da2a92c994b9ed573248e3906e03f16e69fb49d318b328c59"},"schema_version":"1.0","source":{"id":"1309.0574","kind":"arxiv","version":5}},"canonical_sha256":"76066e276b899b6565c7e22ed31a75a5432d135e03b60fb3ac6af7883ea8a09f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76066e276b899b6565c7e22ed31a75a5432d135e03b60fb3ac6af7883ea8a09f","first_computed_at":"2026-05-18T01:35:05.291966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:05.291966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nC0QEGWuHptvTnBIjvvNaio6G73qrVLbpdQPhzoVVKjp26GT/kioVxbisr06KO3diMp1gUlK872yg3kr+qLMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:05.292628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0574","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:beab8356d0aeb98f828ce5f6fcc4173fd0ba179a46a1af12a25ca5df198fdbd1","sha256:b0cf73b2a2eb47dc0991ca9540de9d6bab99379a08885e31a31ef23da3512388"],"state_sha256":"91221c7b1a6768925a0fe648af98c80a679dd1f971c5d5226287ae7e2372dcae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hBlX9PbVDspI+4CNeilsnlIEDz+i2XT3z90WjyaS/cJ5V4NInqT80fyTn+Yae2Qr6dd+IIWnkkdXgM1exrn/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T02:32:15.984482Z","bundle_sha256":"cf1b687d60303868f2ac836d2f44351716b8f96ba8d263bcf6b937785c9a2a1d"}}