{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5T3XB42Y24VNY5FTLCRCTWJGPY","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":"ad685bd687e9cd974d75b2a845151f2979154d2d59e8ef1ce74b37c66678d9bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-22T16:59:39Z","title_canon_sha256":"57abb9ebdfdb39878e51b4af57804e859c3a0c4baf2562f8b4bd116078a45f72"},"schema_version":"1.0","source":{"id":"1408.5361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5361","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5361v1","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5361","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"5T3XB42Y24VN","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5T3XB42Y24VNY5FT","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5T3XB42Y","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:2b566030a20bb5e3200d3064e921434a4b921bb68d68518aec80d0b018b57995","target":"graph","created_at":"2026-05-18T01:22:21Z","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 $F$ be a field, let $D$ be a subring of $F$ and let $Z$ be an irreducible subspace of the space of all valuation rings between $D$ and $F$ that have quotient field $F$. Then $Z$ is a locally ringed space whose ring of global sections is $A = \\bigcap_{V \\in Z}V$. All rings between $D$ and $F$ that are integrally closed in $F$ arise in such a way. Motivated by applications in areas such as multiplicative ideal theory and real algebraic geometry, a number of authors have formulated criteria for when $A$ is a Pr\\\"ufer domain. We give geometric criteria for when $A$ is a Pr\\\"ufer domain that re","authors_text":"Bruce Olberding","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-22T16:59:39Z","title":"On the geometry of Pr\\\"ufer intersections of valuation rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5361","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:a083676fe0f88cbca69608dad7288c0f3e67f3cd1729da4689dc71ba385004d2","target":"record","created_at":"2026-05-18T01:22:21Z","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":"ad685bd687e9cd974d75b2a845151f2979154d2d59e8ef1ce74b37c66678d9bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-22T16:59:39Z","title_canon_sha256":"57abb9ebdfdb39878e51b4af57804e859c3a0c4baf2562f8b4bd116078a45f72"},"schema_version":"1.0","source":{"id":"1408.5361","kind":"arxiv","version":1}},"canonical_sha256":"ecf770f358d72adc74b358a229d9267e23e8787d68167f53830a51c9456eb2d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecf770f358d72adc74b358a229d9267e23e8787d68167f53830a51c9456eb2d7","first_computed_at":"2026-05-18T01:22:21.845903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:21.845903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BpzCQ0Bq0asHWArX5p5WmfMXwoTSdTjuujXeFUDzEv4oYXUEYXF00+UNmNu13YRwXAOt52N/L/u1ZeVJ+PWqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:21.846719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a083676fe0f88cbca69608dad7288c0f3e67f3cd1729da4689dc71ba385004d2","sha256:2b566030a20bb5e3200d3064e921434a4b921bb68d68518aec80d0b018b57995"],"state_sha256":"eb16eba1d7aa9ab251fe84383e94879bb5e713970904e86c66bd6fe479f0732c"}