{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ODEPDKLGNVHL7PEIIPDWKOJZD6","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":"6e55104bdd3f6a3387fc880531566773a58166cf70b197fdfd1ebceb3b2fd226","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-06-13T22:20:05Z","title_canon_sha256":"2edabf176aa807f329641fa002fb9715b169e886d125e98fe3ff465bf40445dc"},"schema_version":"1.0","source":{"id":"1706.04270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04270","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04270v1","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04270","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"ODEPDKLGNVHL","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"ODEPDKLGNVHL7PEI","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"ODEPDKLG","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:b3b33ee3296653c8c96e9bd922623cce9d93b0e8bd8b6be4754ceb848284e1c5","target":"graph","created_at":"2026-05-18T00:42:23Z","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":"The reticulation of an algebra $A$ is a bounded distributive lattice ${\\cal L}(A)$ whose prime spectrum of filters or ideals is homeomorphic to the prime spectrum of congruences of $A$, endowed with the Stone topologies. We have obtained a construction for the reticulation of any algebra $A$ from a semi-degenerate congruence-modular variety ${\\cal C}$ in the case when the commutator of $A$, applied to compact congruences of $A$, produces compact congruences, in particular when ${\\cal C}$ has principal commutators; furthermore, it turns out that weaker conditions than the fact that $A$ belongs ","authors_text":"Claudia Mure\\c{s}an, George Georgescu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-06-13T22:20:05Z","title":"The Reticulation of a Universal Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04270","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":"sha256:3b9ef68550f54c82853ee09063a9165166abc759473d9963c8bc3779fba87ea0","target":"record","created_at":"2026-05-18T00:42:23Z","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":"6e55104bdd3f6a3387fc880531566773a58166cf70b197fdfd1ebceb3b2fd226","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-06-13T22:20:05Z","title_canon_sha256":"2edabf176aa807f329641fa002fb9715b169e886d125e98fe3ff465bf40445dc"},"schema_version":"1.0","source":{"id":"1706.04270","kind":"arxiv","version":1}},"canonical_sha256":"70c8f1a9666d4ebfbc8843c76539391fbfb5db0dd7e36717023cb98bed581a3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70c8f1a9666d4ebfbc8843c76539391fbfb5db0dd7e36717023cb98bed581a3e","first_computed_at":"2026-05-18T00:42:23.114237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:23.114237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XVqMKhZ43KR6a+Jd7iC58/1+NsWyZX+qKImogfjv/j/UNAedX2znAp8V6TqUtv0uc699iiqvpQq1QfKPcFG9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:23.114709Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b9ef68550f54c82853ee09063a9165166abc759473d9963c8bc3779fba87ea0","sha256:b3b33ee3296653c8c96e9bd922623cce9d93b0e8bd8b6be4754ceb848284e1c5"],"state_sha256":"e5485bc85e69623e8561ff3d586718f888ff973f8e7c401be95a6204d34c0418"}