{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OHF6QF3ZWTQYDEQFF5E547ZKTN","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":"54e1236f0c4ecdd02f1be8140022d4ee04a1a44dbdb4d564d3da37ba5579d53e","cross_cats_sorted":["math.CT","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-10-08T15:39:29Z","title_canon_sha256":"34a27ca908ef98077773c0bce5c47801385cac207d08d20dc619da571ecf98ab"},"schema_version":"1.0","source":{"id":"1310.2175","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2175","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2175v1","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2175","created_at":"2026-05-18T02:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"OHF6QF3ZWTQY","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OHF6QF3ZWTQYDEQF","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OHF6QF3Z","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:fb85423ba3367ab083e1f20f893c6d2a479395558db62cd61f2d46b9d9ae3b0b","target":"graph","created_at":"2026-05-18T02:53:17Z","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 prove that the category of unital hyperarchimedean vector lattices is equivalent to the category of Boolean algebras. The key result needed to establish the equivalence is that, via the Yosida representation, such a vector lattice is naturally isomorphic to the vector lattice of all locally constant real-valued continuous functions on a Boolean (=compact Hausdorff totally disconnected) space. We give two applications of our main result.","authors_text":"Richard N. Ball, Vincenzo Marra","cross_cats":["math.CT","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-10-08T15:39:29Z","title":"Unital hyperarchimedean vector lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2175","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":"sha256:1ebde922c6a4f6893abb1ca84fe537ee0459c5caeaeb3fd9daa875eaab90b1f8","target":"record","created_at":"2026-05-18T02:53:17Z","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":"54e1236f0c4ecdd02f1be8140022d4ee04a1a44dbdb4d564d3da37ba5579d53e","cross_cats_sorted":["math.CT","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-10-08T15:39:29Z","title_canon_sha256":"34a27ca908ef98077773c0bce5c47801385cac207d08d20dc619da571ecf98ab"},"schema_version":"1.0","source":{"id":"1310.2175","kind":"arxiv","version":1}},"canonical_sha256":"71cbe81779b4e18192052f49de7f2a9b5bc4e5e9b7088a83478c261cad586599","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71cbe81779b4e18192052f49de7f2a9b5bc4e5e9b7088a83478c261cad586599","first_computed_at":"2026-05-18T02:53:17.488292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:17.488292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tmqkim0TNDdq4p5XgVgkEo7vaIZKlJswl9opQ0MIIXKLccZTYX+JiueUnG1wlAhAU6fO9YtfdtZh9DShStYkBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:17.488794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2175","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ebde922c6a4f6893abb1ca84fe537ee0459c5caeaeb3fd9daa875eaab90b1f8","sha256:fb85423ba3367ab083e1f20f893c6d2a479395558db62cd61f2d46b9d9ae3b0b"],"state_sha256":"2b6f463ae436172454cfeca346a329b5510e56828a7e8acfd3b120886d34d438"}