{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RBXBZTLI2ARKU5Q2AN2BGVGLAN","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":"238588bc3de39a55f5ae58fced7b3f505b8c65b7ae47ba42b14e468b0b255866","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-06-25T13:50:36Z","title_canon_sha256":"9a707aa43fee3c14faac13e319b932c5be351996158098cb786f5611758a9187"},"schema_version":"1.0","source":{"id":"1206.5682","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5682","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5682v2","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5682","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"RBXBZTLI2ARK","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RBXBZTLI2ARKU5Q2","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RBXBZTLI","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:23e7676dd13758e25cdc95ec296b494c07420e71ddddfbaa55636a6dc0d7687d","target":"graph","created_at":"2026-05-18T03:21:43Z","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, for every theory $T$ which is given by an ${\\mathcal L}_{\\omega_1,\\omega}$ sentence, $T$ has less than $2^{\\aleph_0}$ many countable models if and only if we have that, for every $X\\in 2^\\omega$ on a cone of Turing degrees, every $X$-hyperarithmetic model of $T$ has an $X$-computable copy. We also find a concrete description, relative to some oracle, of the Turing-degree spectra of all the models of a counterexample to Vaught's conjecture.","authors_text":"Antonio Montalban","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-06-25T13:50:36Z","title":"A computability theoretic equivalent to Vaught's conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5682","kind":"arxiv","version":2},"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:e2becfce604a7eff6f5c76228cbbac1900ead4febbb44d1953bdcd3cf89ff2dd","target":"record","created_at":"2026-05-18T03:21:43Z","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":"238588bc3de39a55f5ae58fced7b3f505b8c65b7ae47ba42b14e468b0b255866","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-06-25T13:50:36Z","title_canon_sha256":"9a707aa43fee3c14faac13e319b932c5be351996158098cb786f5611758a9187"},"schema_version":"1.0","source":{"id":"1206.5682","kind":"arxiv","version":2}},"canonical_sha256":"886e1ccd68d022aa761a03741354cb034e570010991612a395a69e6a270d6b5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"886e1ccd68d022aa761a03741354cb034e570010991612a395a69e6a270d6b5e","first_computed_at":"2026-05-18T03:21:43.686451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:43.686451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dqyLkwoealLTVJALfz3NhNp1zFa3zOsOsv9SunM1Kw047Mk5HAGlEwGbv4yHe246fSjpzjtqJSFuMAa6xSPGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:43.687213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5682","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2becfce604a7eff6f5c76228cbbac1900ead4febbb44d1953bdcd3cf89ff2dd","sha256:23e7676dd13758e25cdc95ec296b494c07420e71ddddfbaa55636a6dc0d7687d"],"state_sha256":"ea0f1394533095f13e55f2f738cf6c7a11c3618bfbe0b1e57c090575448658ff"}