{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UXUY2LMHKVV36TL2BZQYOD5USI","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":"9dd83e278698fc5fde13c071ee48587ac3ffae756436b08b5b5808b2f75f54c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-02T14:41:42Z","title_canon_sha256":"0bbe48e5d3b97f9556868b259f0b61c39c8aa3b4a2de582e729acfef0861ea98"},"schema_version":"1.0","source":{"id":"1804.00565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00565","created_at":"2026-05-17T23:57:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00565v1","created_at":"2026-05-17T23:57:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00565","created_at":"2026-05-17T23:57:21Z"},{"alias_kind":"pith_short_12","alias_value":"UXUY2LMHKVV3","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UXUY2LMHKVV36TL2","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UXUY2LMH","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:f37c7d463f8101231626f1d138a55e2c7335f95403e0b1177dbdf43fe0fdf7c0","target":"graph","created_at":"2026-05-17T23:57:21Z","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":"An explicit categorical equivalence is defined between a proper subvariety of the class of $PMV$-algebras, as defined by Di Nola and Dvure$\\check{c}$enskij, to be called $PMV_f$-algebras, and the category of semi-low $f_u$-rings. This categorical representation is done using the prime spectrum of the $MV$-algebras, through the equivalence between $MV$-algebras and $l_u$-groups established by Mundici, from the perspective of the Dubuc-Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low $f_u$-rings associated to Boolean algebras are character","authors_text":"Lilian J. Cruz, Yuri A. Poveda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-02T14:41:42Z","title":"Categorical Equivalence between $PMV_f$- product algebras and semi-low $f_u$-rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00565","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":"sha256:64de2884ebf03abeab9c8b058cc4fb3136874a138c3e9200331fb5c873e22677","target":"record","created_at":"2026-05-17T23:57:21Z","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":"9dd83e278698fc5fde13c071ee48587ac3ffae756436b08b5b5808b2f75f54c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-02T14:41:42Z","title_canon_sha256":"0bbe48e5d3b97f9556868b259f0b61c39c8aa3b4a2de582e729acfef0861ea98"},"schema_version":"1.0","source":{"id":"1804.00565","kind":"arxiv","version":1}},"canonical_sha256":"a5e98d2d87556bbf4d7a0e61870fb49228f893853d82312355d31f93b23a04f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5e98d2d87556bbf4d7a0e61870fb49228f893853d82312355d31f93b23a04f2","first_computed_at":"2026-05-17T23:57:21.632058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:21.632058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nLOfvPePHVoyIh8y4PKuq6H6tPpD6blLFebWzCC++kSjoaXAubRfjEO5xOC7UlgYnZr47g+pFadUzEkc74sOCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:21.632611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64de2884ebf03abeab9c8b058cc4fb3136874a138c3e9200331fb5c873e22677","sha256:f37c7d463f8101231626f1d138a55e2c7335f95403e0b1177dbdf43fe0fdf7c0"],"state_sha256":"e5388c2538e59883cd8d47601b34b5a59402a1b81d519b32c6bbcfd345ab7895"}