{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YX3SWTDJJZLNURYVNFO2MBKPUI","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":"ac72dc9a2c88dc032eb2c59fe36f6c18742fbee7680568e7b300c1f419bd0371","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-12-10T16:34:03Z","title_canon_sha256":"b0f25c106ec487bf89f24cd05d4ce0916113dd55aa0f6b48dfbbd47d3dc389bd"},"schema_version":"1.0","source":{"id":"1512.03312","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03312","created_at":"2026-05-18T01:15:51Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03312v2","created_at":"2026-05-18T01:15:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03312","created_at":"2026-05-18T01:15:51Z"},{"alias_kind":"pith_short_12","alias_value":"YX3SWTDJJZLN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YX3SWTDJJZLNURYV","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YX3SWTDJ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:00e90d7ab8075a6e51a0259474d4da5531660ec7659a3eeeb5c04b4f0d90714c","target":"graph","created_at":"2026-05-18T01:15:51Z","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 consider the lattice-ordered groups Inv$(R)$ and Div$(R)$ of invertible and divisorial fractional ideals of a completely integrally closed Pr\\\"ufer domain. We prove that Div$(R)$ is the completion of the group Inv$(R)$, and we show there is a faithfully flat extension $S$ of $R$ such that $S$ is a completely integrally closed B\\'ezout domain with Div$(R) \\cong $ Inv$(S)$. Among the class of completely integrally closed Pr\\\"ufer domains, we focus on the one-dimensional Pr\\\"ufer domains. This class includes Dedekind domains, the latter being the one-dimensional Pr\\\"ufer domains whose maximal ","authors_text":"Andreas Reinhart, Bruce Olberding, Olivier A. Heubo-Kwegna","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-12-10T16:34:03Z","title":"Group-theoretic and topological invariants of completely integrally closed Pr\\\"ufer domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03312","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":"sha256:93b17fbbea593397733dff5116e3f338dad87fdc5b6fd8aeedd31212e8c175a4","target":"record","created_at":"2026-05-18T01:15:51Z","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":"ac72dc9a2c88dc032eb2c59fe36f6c18742fbee7680568e7b300c1f419bd0371","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-12-10T16:34:03Z","title_canon_sha256":"b0f25c106ec487bf89f24cd05d4ce0916113dd55aa0f6b48dfbbd47d3dc389bd"},"schema_version":"1.0","source":{"id":"1512.03312","kind":"arxiv","version":2}},"canonical_sha256":"c5f72b4c694e56da4715695da6054fa21048b857ed9375e017d924524c942af2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5f72b4c694e56da4715695da6054fa21048b857ed9375e017d924524c942af2","first_computed_at":"2026-05-18T01:15:51.775926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:51.775926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ERMF+Ayf4qRFEV1Q4xDz1DtRfVLhhdTTaaFABhf2w7Ihvu1S3MeitrQjoZ73RC8ye9ROwLxl840uHwjazQriBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:51.776309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03312","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93b17fbbea593397733dff5116e3f338dad87fdc5b6fd8aeedd31212e8c175a4","sha256:00e90d7ab8075a6e51a0259474d4da5531660ec7659a3eeeb5c04b4f0d90714c"],"state_sha256":"1831998be7c1cd2ad7a7512fde1198a07d132527e3da51c63daab429479e271e"}