{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NPOIYNDKOIMU6H5XEBY67FBCJP","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":"77cfd3936a695cdd7c60a10d067261ec3bd7e8290809e1fb7ea23262658358b9","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-02-11T16:54:09Z","title_canon_sha256":"f4507dc324aa6f10670f02336328cffa3c05c13934c08993f85b63c5e1635a4a"},"schema_version":"1.0","source":{"id":"1202.2451","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2451","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2451v1","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2451","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"pith_short_12","alias_value":"NPOIYNDKOIMU","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NPOIYNDKOIMU6H5X","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NPOIYNDK","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:354ce98d0bc346364ccd3cf71c68198286ec9ea3657a8915dece29c6065b9a2c","target":"graph","created_at":"2026-05-18T04:02:26Z","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 $K$ be a field and let $A$ be a subring of $K$. We consider properties and applications of a compact, Hausdorff topology called the \"ultrafilter topology\" defined on the space Zar$(K|A)$ of all valuation domains having $K$ as quotient field and containing $A$. We show that the ultrafilter topology coincides with the constructible topology on the abstract Riemann-Zariski surface Zar$(K|A)$. We extend results regarding distinguished spectral topologies on spaces of valuation domains.","authors_text":"Carmelo A. Finocchiaro, K. Alan Loper, Marco Fontana","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-02-11T16:54:09Z","title":"Ultrafilter and Constructible topologies on spaces of valuation domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2451","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:f66ac77194f6392aef04a11a9e981b9adb5e016d11bf89a756fede4e1101dafe","target":"record","created_at":"2026-05-18T04:02:26Z","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":"77cfd3936a695cdd7c60a10d067261ec3bd7e8290809e1fb7ea23262658358b9","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-02-11T16:54:09Z","title_canon_sha256":"f4507dc324aa6f10670f02336328cffa3c05c13934c08993f85b63c5e1635a4a"},"schema_version":"1.0","source":{"id":"1202.2451","kind":"arxiv","version":1}},"canonical_sha256":"6bdc8c346a72194f1fb72071ef94224bf9c67e286e77adcfec341f5c082ec004","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bdc8c346a72194f1fb72071ef94224bf9c67e286e77adcfec341f5c082ec004","first_computed_at":"2026-05-18T04:02:26.493038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:26.493038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WQXsyLHwvO+T27fyoxiSwbEY2CzfT3FEnGidMzSk3Pdt42XCXtt720cLSpR7Bo+zu+6RjiYuGd6fzgANNKrIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:26.493535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2451","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f66ac77194f6392aef04a11a9e981b9adb5e016d11bf89a756fede4e1101dafe","sha256:354ce98d0bc346364ccd3cf71c68198286ec9ea3657a8915dece29c6065b9a2c"],"state_sha256":"d4deaa1eddbd128851da8e08c53b16ac200993666114e2b5cc117c9b5546bb8f"}