{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:37MLOMNORDUJ447X5IG4CAVXD2","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":"c2fea23c914b589c26fdf6f485f68d0d10d712d8c63a2a46c29ace9836b18a9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-01T17:37:20Z","title_canon_sha256":"d0982313dc6d26948fcb9f2196e66b6b128cc09ba31f2f0896e1a5bf37c52cc3"},"schema_version":"1.0","source":{"id":"1503.00318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00318","created_at":"2026-05-18T02:25:54Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00318v1","created_at":"2026-05-18T02:25:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00318","created_at":"2026-05-18T02:25:54Z"},{"alias_kind":"pith_short_12","alias_value":"37MLOMNORDUJ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"37MLOMNORDUJ447X","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"37MLOMNO","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:95bd370245e862d19acf3e48794cc7b5b93c4b5e4ec4c4794c38d07c5a8c1912","target":"graph","created_at":"2026-05-18T02:25:54Z","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 introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of $L_{\\omega_1,\\omega}$. Theorem: Let $T$ be any complete first-order theory in a countable language with an atomic model. If the pseudo-minimal types are not dense, then there are $2^{\\aleph_1}$ pairwise non-isomorphic atomic models of $T$, each of size $\\aleph_1$.","authors_text":"Jerusalem), John T. Baldwin (U. Ill. Chicago), Michael C. Laskowski (U. of Maryland), Saharon Shelah (Hebrew University","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-01T17:37:20Z","title":"Constructing many atomic models in $\\aleph_1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00318","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:eaccd275751665acf75d45b6761c61d5fa37dcd54d0e3e6bd539bea8d3a445fd","target":"record","created_at":"2026-05-18T02:25:54Z","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":"c2fea23c914b589c26fdf6f485f68d0d10d712d8c63a2a46c29ace9836b18a9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-01T17:37:20Z","title_canon_sha256":"d0982313dc6d26948fcb9f2196e66b6b128cc09ba31f2f0896e1a5bf37c52cc3"},"schema_version":"1.0","source":{"id":"1503.00318","kind":"arxiv","version":1}},"canonical_sha256":"dfd8b731ae88e89e73f7ea0dc102b71ea36ff1600d6a9e4fae32d45a6cfd2308","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfd8b731ae88e89e73f7ea0dc102b71ea36ff1600d6a9e4fae32d45a6cfd2308","first_computed_at":"2026-05-18T02:25:54.681525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:54.681525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iOWirs5bPoaJReuzv9ED+LxfaBb8ZPy2MlHyDthIWHqA7WX7kEvqTM3JfuqU3ySWJjOEt5p03Od2KuS+QbWfBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:54.681924Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eaccd275751665acf75d45b6761c61d5fa37dcd54d0e3e6bd539bea8d3a445fd","sha256:95bd370245e862d19acf3e48794cc7b5b93c4b5e4ec4c4794c38d07c5a8c1912"],"state_sha256":"7633513a63f7cfc033786055fe418bc1191fb39fedeb928a9910af22ef067de9"}