{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:UOKCPFRGOW4OX3OE4JIR4L7L2H","short_pith_number":"pith:UOKCPFRG","canonical_record":{"source":{"id":"1009.1056","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-06T13:49:55Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"041c84cc69a9c4713457cc392f765b63abd171cb70896bed0e52eef96ce17bc4","abstract_canon_sha256":"1fbd7e8e906399b7eeb8ecfba5e1a1ac8dec3f849f2784d5d72a4e75ae65c8a0"},"schema_version":"1.0"},"canonical_sha256":"a39427962675b8ebedc4e2511e2febd1f402feb098e45e49df0b963f2694d012","source":{"kind":"arxiv","id":"1009.1056","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1056","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1056v2","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1056","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"pith_short_12","alias_value":"UOKCPFRGOW4O","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UOKCPFRGOW4OX3OE","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UOKCPFRG","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:UOKCPFRGOW4OX3OE4JIR4L7L2H","target":"record","payload":{"canonical_record":{"source":{"id":"1009.1056","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-06T13:49:55Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"041c84cc69a9c4713457cc392f765b63abd171cb70896bed0e52eef96ce17bc4","abstract_canon_sha256":"1fbd7e8e906399b7eeb8ecfba5e1a1ac8dec3f849f2784d5d72a4e75ae65c8a0"},"schema_version":"1.0"},"canonical_sha256":"a39427962675b8ebedc4e2511e2febd1f402feb098e45e49df0b963f2694d012","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:37.798077Z","signature_b64":"irXW4Xl8fuggItY/bY55NPMcypujquAcvKAyvRUYntCL1Ny61HYivtAHaCrKrW1J1quvLXEFkv/OMvWYuEVFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a39427962675b8ebedc4e2511e2febd1f402feb098e45e49df0b963f2694d012","last_reissued_at":"2026-05-18T04:25:37.797624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:37.797624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.1056","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":"2026-05-18T04:25:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VHdUIPLwU/O65Vvc9507K23whlr4OgdEYFd7BUV+csnJ6Exo9EPtDb50FjegvPXsIO2mZrbqwRN2Y1wpjjAQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:55:54.796629Z"},"content_sha256":"4a8b58216d05ce5a42995aa26b15c2f57398a14c2746cf1d83f38fb196692e01","schema_version":"1.0","event_id":"sha256:4a8b58216d05ce5a42995aa26b15c2f57398a14c2746cf1d83f38fb196692e01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:UOKCPFRGOW4OX3OE4JIR4L7L2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniformly rigid spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Christian Kappen","submitted_at":"2010-09-06T13:49:55Z","abstract_excerpt":"We define a new category of non-archimedean analytic spaces over a complete discretely valued field, which we call uniformly rigid. It extends the category of rigid spaces, and it can be described in terms of bounded functions on products of open and closed polydiscs. We relate uniformly rigid spaces to their associated classical rigid spaces, and we transfer various constructions and results from rigid geometry to the uniformly rigid setting. In particular, we prove an analog of Kiehl's patching theorem for coherent ideals, and we define the uniformly rigid generic fiber of a formal scheme of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1056","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":""},"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":"2026-05-18T04:25:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w7UT02+tmz1vrNQciy7KBzURAK8Mg20tJlvanxNPDI/zE5hi9jc38mixihd/qpdHYH4dgvgE1M2CKUIMDMXtAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:55:54.797347Z"},"content_sha256":"11dee17e5f72134ab4cacaf24e871661e40e2a63bbe6b4b334003bab7a66786c","schema_version":"1.0","event_id":"sha256:11dee17e5f72134ab4cacaf24e871661e40e2a63bbe6b4b334003bab7a66786c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UOKCPFRGOW4OX3OE4JIR4L7L2H/bundle.json","state_url":"https://pith.science/pith/UOKCPFRGOW4OX3OE4JIR4L7L2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UOKCPFRGOW4OX3OE4JIR4L7L2H/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":"2026-06-07T17:55:54Z","links":{"resolver":"https://pith.science/pith/UOKCPFRGOW4OX3OE4JIR4L7L2H","bundle":"https://pith.science/pith/UOKCPFRGOW4OX3OE4JIR4L7L2H/bundle.json","state":"https://pith.science/pith/UOKCPFRGOW4OX3OE4JIR4L7L2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UOKCPFRGOW4OX3OE4JIR4L7L2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UOKCPFRGOW4OX3OE4JIR4L7L2H","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":"1fbd7e8e906399b7eeb8ecfba5e1a1ac8dec3f849f2784d5d72a4e75ae65c8a0","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-06T13:49:55Z","title_canon_sha256":"041c84cc69a9c4713457cc392f765b63abd171cb70896bed0e52eef96ce17bc4"},"schema_version":"1.0","source":{"id":"1009.1056","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1056","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1056v2","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1056","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"pith_short_12","alias_value":"UOKCPFRGOW4O","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UOKCPFRGOW4OX3OE","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UOKCPFRG","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:11dee17e5f72134ab4cacaf24e871661e40e2a63bbe6b4b334003bab7a66786c","target":"graph","created_at":"2026-05-18T04:25:37Z","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 define a new category of non-archimedean analytic spaces over a complete discretely valued field, which we call uniformly rigid. It extends the category of rigid spaces, and it can be described in terms of bounded functions on products of open and closed polydiscs. We relate uniformly rigid spaces to their associated classical rigid spaces, and we transfer various constructions and results from rigid geometry to the uniformly rigid setting. In particular, we prove an analog of Kiehl's patching theorem for coherent ideals, and we define the uniformly rigid generic fiber of a formal scheme of","authors_text":"Christian Kappen","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-06T13:49:55Z","title":"Uniformly rigid spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1056","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":"sha256:4a8b58216d05ce5a42995aa26b15c2f57398a14c2746cf1d83f38fb196692e01","target":"record","created_at":"2026-05-18T04:25:37Z","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":"1fbd7e8e906399b7eeb8ecfba5e1a1ac8dec3f849f2784d5d72a4e75ae65c8a0","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-06T13:49:55Z","title_canon_sha256":"041c84cc69a9c4713457cc392f765b63abd171cb70896bed0e52eef96ce17bc4"},"schema_version":"1.0","source":{"id":"1009.1056","kind":"arxiv","version":2}},"canonical_sha256":"a39427962675b8ebedc4e2511e2febd1f402feb098e45e49df0b963f2694d012","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a39427962675b8ebedc4e2511e2febd1f402feb098e45e49df0b963f2694d012","first_computed_at":"2026-05-18T04:25:37.797624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:37.797624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"irXW4Xl8fuggItY/bY55NPMcypujquAcvKAyvRUYntCL1Ny61HYivtAHaCrKrW1J1quvLXEFkv/OMvWYuEVFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:37.798077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1056","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a8b58216d05ce5a42995aa26b15c2f57398a14c2746cf1d83f38fb196692e01","sha256:11dee17e5f72134ab4cacaf24e871661e40e2a63bbe6b4b334003bab7a66786c"],"state_sha256":"086047f17f0e4322b280130586e53f6b6c8eb5fedfaaaa3193ef7db5caec2ef7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"37frQ16f/kXrZ6UGmETV2faSZiREouj2WWaI1aYSTyWx6eiVP/G1B2z3OQ/9bBN+0Af3afBhgt+O1bd712vLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:55:54.801665Z","bundle_sha256":"30994d7e17522ad6efd33fd72659749bfe82a9c8b8649c3915615faf28a6c025"}}