{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BOVKP2HZJ4NIEV76G75QKFJ2CF","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":"758879858d1dfb77c120066cba73f7e79bfbd8f07b95f70fbb0fb578d6194e1f","cross_cats_sorted":["math.AC","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-03-01T17:12:09Z","title_canon_sha256":"396e686b45d8b7584200d5767655963121b9d54b92b5009a0fa13a5a665243ad"},"schema_version":"1.0","source":{"id":"1903.00414","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00414","created_at":"2026-07-05T00:42:51Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00414v5","created_at":"2026-07-05T00:42:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00414","created_at":"2026-07-05T00:42:51Z"},{"alias_kind":"pith_short_12","alias_value":"BOVKP2HZJ4NI","created_at":"2026-07-05T00:42:51Z"},{"alias_kind":"pith_short_16","alias_value":"BOVKP2HZJ4NIEV76","created_at":"2026-07-05T00:42:51Z"},{"alias_kind":"pith_short_8","alias_value":"BOVKP2HZ","created_at":"2026-07-05T00:42:51Z"}],"graph_snapshots":[{"event_id":"sha256:26cd3bf765fd53db036f8149dab530f40f9cce5b66be008860279f1bc07d8c01","target":"graph","created_at":"2026-07-05T00:42:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1903.00414/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that certain classes of modules have universal models with respect to pure embeddings.\n  $Theorem.$ Let $R$ be a ring, $T$ a first-order theory with an infinite model extending the theory of $R$-modules and $K^T=(Mod(T), \\leq_{pp})$ (where $\\leq_{pp}$ stands for pure submodule). Assume $K^T$ has joint embedding and amalgamation.\n  If $\\lambda^{|T|}=\\lambda$ or $\\forall \\mu < \\lambda( \\mu^{|T|} < \\lambda)$, then $K^T$ has a universal model of cardinality $\\lambda$.\n  As a special case we get a recent result of Shelah [Sh17, 1.2] concerning the existence of universal reduced torsion-free","authors_text":"Marcos Mazari-Armida, Thomas G. Kucera","cross_cats":["math.AC","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-03-01T17:12:09Z","title":"On universal modules with pure embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00414","kind":"arxiv","version":5},"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:ea270ac31b3e87108ecbe985fbc10ad5d8db5829d3ea5370bd0f493ff465253b","target":"record","created_at":"2026-07-05T00:42:51Z","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":"758879858d1dfb77c120066cba73f7e79bfbd8f07b95f70fbb0fb578d6194e1f","cross_cats_sorted":["math.AC","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-03-01T17:12:09Z","title_canon_sha256":"396e686b45d8b7584200d5767655963121b9d54b92b5009a0fa13a5a665243ad"},"schema_version":"1.0","source":{"id":"1903.00414","kind":"arxiv","version":5}},"canonical_sha256":"0baaa7e8f94f1a8257fe37fb05153a114261e6b79e1dd9fbbece7531d4436dda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0baaa7e8f94f1a8257fe37fb05153a114261e6b79e1dd9fbbece7531d4436dda","first_computed_at":"2026-07-05T00:42:51.970912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:42:51.970912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"omifmDUTEV/EM0k87/rb470nCXQ/BalZxquIlQUgEr1BamfZP2XAroQVvGiLvIs6XMf3bPQ/LoLcW+dWaibWAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:42:51.971468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00414","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea270ac31b3e87108ecbe985fbc10ad5d8db5829d3ea5370bd0f493ff465253b","sha256:26cd3bf765fd53db036f8149dab530f40f9cce5b66be008860279f1bc07d8c01"],"state_sha256":"a89f8e6ce9d8ac4882a31d7c59cc7d6567ba695b692b915746af55f49f062175"}