{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XHGSBKXTG2U4ZZLZXWBN4YKBYW","short_pith_number":"pith:XHGSBKXT","canonical_record":{"source":{"id":"1107.3414","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-18T12:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"c6016149c63476c15cdda2a9bd87d65e11b7078edf7c9310f60f59092fa01701","abstract_canon_sha256":"07f72fb053cf3a3511147ac892c0116bb4ac39367606486edc1f7ce653ff23c1"},"schema_version":"1.0"},"canonical_sha256":"b9cd20aaf336a9cce579bd82de6141c5a40c0a002f4f4a4ea728294f08995ed3","source":{"kind":"arxiv","id":"1107.3414","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3414","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3414v2","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3414","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"pith_short_12","alias_value":"XHGSBKXTG2U4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XHGSBKXTG2U4ZZLZ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XHGSBKXT","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XHGSBKXTG2U4ZZLZXWBN4YKBYW","target":"record","payload":{"canonical_record":{"source":{"id":"1107.3414","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-18T12:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"c6016149c63476c15cdda2a9bd87d65e11b7078edf7c9310f60f59092fa01701","abstract_canon_sha256":"07f72fb053cf3a3511147ac892c0116bb4ac39367606486edc1f7ce653ff23c1"},"schema_version":"1.0"},"canonical_sha256":"b9cd20aaf336a9cce579bd82de6141c5a40c0a002f4f4a4ea728294f08995ed3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:39.452545Z","signature_b64":"JdsNBsQTtWFOhXbJK4peqhccOXBdUXpp2LKJgPgKFs76TYQ1UaGwUBeV0xwYd+Q02x1mxiCFs65RQwG6SyoBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9cd20aaf336a9cce579bd82de6141c5a40c0a002f4f4a4ea728294f08995ed3","last_reissued_at":"2026-05-18T04:11:39.452142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:39.452142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.3414","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":"2026-05-18T04:11:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rM4a977kAiv2CmcMsoT65L6194XrgqguP9mpVAyYfCIMaP7BhCte+Axj5Cb+ybecLkD3Zrmcxt6VGmq72n4/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:33:32.665082Z"},"content_sha256":"3e1a299efcc2c55943a9bf56feb2d3e47f3cc0f3e4f16e337d85dc306ffddd31","schema_version":"1.0","event_id":"sha256:3e1a299efcc2c55943a9bf56feb2d3e47f3cc0f3e4f16e337d85dc306ffddd31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XHGSBKXTG2U4ZZLZXWBN4YKBYW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nagata embedding and A-schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Satoshi Takagi","submitted_at":"2011-07-18T12:24:02Z","abstract_excerpt":"We define the notion of normal A-schemes, and approximable A-schemes. Approximable A-schemes inherit many good properties of ordinary schemes. As a consequence, we see that the Zariski-Riemann space can be regarded in two ways -- either as the limit space of admissible blow ups, or as the universal compactification of the given non-proper scheme. We can prove Nagata embedding using Zariski-Riemann spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3414","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":"2026-05-18T04:11:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2ZkG0ax/JzftpTq6kmKCsmnCRhxvtgzQ7DW8xN6HFeT8+A0O4Qi6UeJmwRN8RMf+/SiTmRePRvjmCPuOTBkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:33:32.665456Z"},"content_sha256":"ee2a64144ff049acf0961a0492f9a5f459ec4886e757cd0f58b52066a21b4960","schema_version":"1.0","event_id":"sha256:ee2a64144ff049acf0961a0492f9a5f459ec4886e757cd0f58b52066a21b4960"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XHGSBKXTG2U4ZZLZXWBN4YKBYW/bundle.json","state_url":"https://pith.science/pith/XHGSBKXTG2U4ZZLZXWBN4YKBYW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XHGSBKXTG2U4ZZLZXWBN4YKBYW/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":"2026-06-04T23:33:32Z","links":{"resolver":"https://pith.science/pith/XHGSBKXTG2U4ZZLZXWBN4YKBYW","bundle":"https://pith.science/pith/XHGSBKXTG2U4ZZLZXWBN4YKBYW/bundle.json","state":"https://pith.science/pith/XHGSBKXTG2U4ZZLZXWBN4YKBYW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XHGSBKXTG2U4ZZLZXWBN4YKBYW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XHGSBKXTG2U4ZZLZXWBN4YKBYW","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":"07f72fb053cf3a3511147ac892c0116bb4ac39367606486edc1f7ce653ff23c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-18T12:24:02Z","title_canon_sha256":"c6016149c63476c15cdda2a9bd87d65e11b7078edf7c9310f60f59092fa01701"},"schema_version":"1.0","source":{"id":"1107.3414","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3414","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3414v2","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3414","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"pith_short_12","alias_value":"XHGSBKXTG2U4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XHGSBKXTG2U4ZZLZ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XHGSBKXT","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:ee2a64144ff049acf0961a0492f9a5f459ec4886e757cd0f58b52066a21b4960","target":"graph","created_at":"2026-05-18T04:11:39Z","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 the notion of normal A-schemes, and approximable A-schemes. Approximable A-schemes inherit many good properties of ordinary schemes. As a consequence, we see that the Zariski-Riemann space can be regarded in two ways -- either as the limit space of admissible blow ups, or as the universal compactification of the given non-proper scheme. We can prove Nagata embedding using Zariski-Riemann spaces.","authors_text":"Satoshi Takagi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-18T12:24:02Z","title":"Nagata embedding and A-schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3414","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":"sha256:3e1a299efcc2c55943a9bf56feb2d3e47f3cc0f3e4f16e337d85dc306ffddd31","target":"record","created_at":"2026-05-18T04:11:39Z","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":"07f72fb053cf3a3511147ac892c0116bb4ac39367606486edc1f7ce653ff23c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-18T12:24:02Z","title_canon_sha256":"c6016149c63476c15cdda2a9bd87d65e11b7078edf7c9310f60f59092fa01701"},"schema_version":"1.0","source":{"id":"1107.3414","kind":"arxiv","version":2}},"canonical_sha256":"b9cd20aaf336a9cce579bd82de6141c5a40c0a002f4f4a4ea728294f08995ed3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9cd20aaf336a9cce579bd82de6141c5a40c0a002f4f4a4ea728294f08995ed3","first_computed_at":"2026-05-18T04:11:39.452142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:39.452142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JdsNBsQTtWFOhXbJK4peqhccOXBdUXpp2LKJgPgKFs76TYQ1UaGwUBeV0xwYd+Q02x1mxiCFs65RQwG6SyoBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:39.452545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3414","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e1a299efcc2c55943a9bf56feb2d3e47f3cc0f3e4f16e337d85dc306ffddd31","sha256:ee2a64144ff049acf0961a0492f9a5f459ec4886e757cd0f58b52066a21b4960"],"state_sha256":"8f081d7828ddb93e611099070edfb755059bff438529addf2d363c77442a746c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vyUoNIbd7M9kE3jegYnIM6zUKiy3iSXK7YAi92TSX8YaFUe3gRQelBMY2kMcFAfnphWwWb4TnZMGeBzjazqMCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:33:32.667286Z","bundle_sha256":"d6d0f64a4da12cbd4c02b11d110c1a5d77bcd49456bf7aa0d0d7598d35070c58"}}