{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:N4N5Q7AGF6W24NRLWJMAIL5BYM","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":"a8ea00e89c7eee370336a61ac9bc4d816fc663d13ad5a6b0ffd018e7915243b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-10T21:10:02Z","title_canon_sha256":"ec039ef056c5b442cef61f84946cc28613fe402806612d460fae551babde2693"},"schema_version":"1.0","source":{"id":"1103.2139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2139","created_at":"2026-05-18T04:26:56Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2139v1","created_at":"2026-05-18T04:26:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2139","created_at":"2026-05-18T04:26:56Z"},{"alias_kind":"pith_short_12","alias_value":"N4N5Q7AGF6W2","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N4N5Q7AGF6W24NRL","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N4N5Q7AG","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:00e25a57efa50ce8086af25d9291158da6d782f24c0f11f51fd6a1f94261887e","target":"graph","created_at":"2026-05-18T04:26:56Z","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":"Let $X$ be a ringed space together with the data $M$ of a set $M_x$ of prime ideals of $\\O_{X,x}$ for each point $x \\in X$. We introduce the localization of $(X,M)$, which is a locally ringed space $Y$ and a map of ringed spaces $Y \\to X$ enjoying a universal property similar to the localization of a ring at a prime ideal. We use this to prove that the category of locally ringed spaces has all inverse limits, to compare them to the inverse limit in ringed spaces, and to construct a very general $\\Spec$ functor. We conclude with a discussion of relative schemes.","authors_text":"W. D. Gillam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-10T21:10:02Z","title":"Localization of ringed spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2139","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":"sha256:2896631f8a722afde1bbe67b4f83444b5ba335b948e73e07e055e4a3fe5ee753","target":"record","created_at":"2026-05-18T04:26:56Z","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":"a8ea00e89c7eee370336a61ac9bc4d816fc663d13ad5a6b0ffd018e7915243b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-10T21:10:02Z","title_canon_sha256":"ec039ef056c5b442cef61f84946cc28613fe402806612d460fae551babde2693"},"schema_version":"1.0","source":{"id":"1103.2139","kind":"arxiv","version":1}},"canonical_sha256":"6f1bd87c062fadae362bb258042fa1c3024ee65218168786d7ea476eb1dd5ea7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f1bd87c062fadae362bb258042fa1c3024ee65218168786d7ea476eb1dd5ea7","first_computed_at":"2026-05-18T04:26:56.124803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:56.124803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DsXWO4p57G1XKpkyBA5/xP/tpRuL6CsUV42WLEp0x4EAflxHgUhFVxDtFvvnwsVL0MAqC0zIg5VI0BBbw1lnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:56.125255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2896631f8a722afde1bbe67b4f83444b5ba335b948e73e07e055e4a3fe5ee753","sha256:00e25a57efa50ce8086af25d9291158da6d782f24c0f11f51fd6a1f94261887e"],"state_sha256":"ab22bfaf1b29b00b2fc542dfdd5ecca201e104bb905e9a648eeaaa3b08b8b69f"}