{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CVUD4LIM5IRLB4WGPMKOXMQPKX","short_pith_number":"pith:CVUD4LIM","schema_version":"1.0","canonical_sha256":"15683e2d0cea22b0f2c67b14ebb20f55cbd1c4cfe3a9b97acae647585b8d3894","source":{"kind":"arxiv","id":"1509.07545","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic properties of infinite directed unions of local quadratic transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bruce Olberding, Matthew Toeniskoetter, William Heinzer","submitted_at":"2015-09-24T21:47:35Z","abstract_excerpt":"We consider infinite sequences {R_n} of successive local quadratic transforms of a regular local ring. Let S denote the directed union of the sequence of regular local rings R_n. We previously showed the existence of a unique limit point V of the family of order valuation rings of the sequence. In this paper, we examine asymptotic properties of this family of order valuations. We link this asymptotic behavior to ring-theoretic properties of S, namely whether S is archimedean and whether S is completely integrally closed. We construct examples of such S that are archimedean and completely integ"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.07545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-09-24T21:47:35Z","cross_cats_sorted":[],"title_canon_sha256":"220bcfbc282c720257abfe9e779979289dc8132d83e9d79cf0dacf69d5dab031","abstract_canon_sha256":"a3559704cb18fb54dc6e38087a183b6e6dede8f3038cb84d290913de067a4094"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:02.509674Z","signature_b64":"7pKJeKP9SHz4DWVa/v7yoeoREy3FZtyY0LXZxolyI0Ap3XBqtn538DQBnLdJGMFnQzL4UAp71UM159lD8+gTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15683e2d0cea22b0f2c67b14ebb20f55cbd1c4cfe3a9b97acae647585b8d3894","last_reissued_at":"2026-05-18T01:32:02.509146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:02.509146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic properties of infinite directed unions of local quadratic transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bruce Olberding, Matthew Toeniskoetter, William Heinzer","submitted_at":"2015-09-24T21:47:35Z","abstract_excerpt":"We consider infinite sequences {R_n} of successive local quadratic transforms of a regular local ring. Let S denote the directed union of the sequence of regular local rings R_n. We previously showed the existence of a unique limit point V of the family of order valuation rings of the sequence. In this paper, we examine asymptotic properties of this family of order valuations. We link this asymptotic behavior to ring-theoretic properties of S, namely whether S is archimedean and whether S is completely integrally closed. We construct examples of such S that are archimedean and completely integ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07545","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.07545","created_at":"2026-05-18T01:32:02.509224+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.07545v1","created_at":"2026-05-18T01:32:02.509224+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07545","created_at":"2026-05-18T01:32:02.509224+00:00"},{"alias_kind":"pith_short_12","alias_value":"CVUD4LIM5IRL","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CVUD4LIM5IRLB4WG","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CVUD4LIM","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CVUD4LIM5IRLB4WGPMKOXMQPKX","json":"https://pith.science/pith/CVUD4LIM5IRLB4WGPMKOXMQPKX.json","graph_json":"https://pith.science/api/pith-number/CVUD4LIM5IRLB4WGPMKOXMQPKX/graph.json","events_json":"https://pith.science/api/pith-number/CVUD4LIM5IRLB4WGPMKOXMQPKX/events.json","paper":"https://pith.science/paper/CVUD4LIM"},"agent_actions":{"view_html":"https://pith.science/pith/CVUD4LIM5IRLB4WGPMKOXMQPKX","download_json":"https://pith.science/pith/CVUD4LIM5IRLB4WGPMKOXMQPKX.json","view_paper":"https://pith.science/paper/CVUD4LIM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.07545&json=true","fetch_graph":"https://pith.science/api/pith-number/CVUD4LIM5IRLB4WGPMKOXMQPKX/graph.json","fetch_events":"https://pith.science/api/pith-number/CVUD4LIM5IRLB4WGPMKOXMQPKX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CVUD4LIM5IRLB4WGPMKOXMQPKX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CVUD4LIM5IRLB4WGPMKOXMQPKX/action/storage_attestation","attest_author":"https://pith.science/pith/CVUD4LIM5IRLB4WGPMKOXMQPKX/action/author_attestation","sign_citation":"https://pith.science/pith/CVUD4LIM5IRLB4WGPMKOXMQPKX/action/citation_signature","submit_replication":"https://pith.science/pith/CVUD4LIM5IRLB4WGPMKOXMQPKX/action/replication_record"}},"created_at":"2026-05-18T01:32:02.509224+00:00","updated_at":"2026-05-18T01:32:02.509224+00:00"}