{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:56TNFAZOC3OQ7IXFILO2LRCMEC","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":"a6d9a2e7bae546409a2851a80f65bf7a89282fdd8b219c2e8c01d091acc3ed80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-30T06:25:41Z","title_canon_sha256":"3a62457e7bc960c9e6fac43cd3b728176ff1e91e77d1785907f626d2637b355f"},"schema_version":"1.0","source":{"id":"1810.12542","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12542","created_at":"2026-05-18T00:01:06Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12542v2","created_at":"2026-05-18T00:01:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12542","created_at":"2026-05-18T00:01:06Z"},{"alias_kind":"pith_short_12","alias_value":"56TNFAZOC3OQ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"56TNFAZOC3OQ7IXF","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"56TNFAZO","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:9da1d9ed8918715e8488243628873738a2fc39ad153777213cc535576465e9b4","target":"graph","created_at":"2026-05-18T00:01:06Z","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":"In a handwtitten note of 1975, Leo Harrington sketched a construction of a model of ZFC (no large cardinals or anything beyond ZFC!) in which $\\mathbf\\Pi^1_3$-Separation holds but $\\mathbf\\Sigma^1_3$-Reduction fails. The result has never appeared in a journal or book publication except for a few of old references.","authors_text":"Vassily Lyubetsky, Vladimir Kanovei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-30T06:25:41Z","title":"On Harrington's model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12542","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:c4929744476a8853c6be07209ff96983926c8ae552efd7b1da04c120d4108807","target":"record","created_at":"2026-05-18T00:01:06Z","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":"a6d9a2e7bae546409a2851a80f65bf7a89282fdd8b219c2e8c01d091acc3ed80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-30T06:25:41Z","title_canon_sha256":"3a62457e7bc960c9e6fac43cd3b728176ff1e91e77d1785907f626d2637b355f"},"schema_version":"1.0","source":{"id":"1810.12542","kind":"arxiv","version":2}},"canonical_sha256":"efa6d2832e16dd0fa2e542dda5c44c20a3f9702c7a2931fad89286f928b38afe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efa6d2832e16dd0fa2e542dda5c44c20a3f9702c7a2931fad89286f928b38afe","first_computed_at":"2026-05-18T00:01:06.585255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:06.585255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eKaXp5a5dglrTTx+gqC/efL7lLwFsvGa44BDl1prEnVfuyJcqPxFwfz+jBtfrEfV9jhFdrpxMSnTw2DYZ9fmCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:06.585714Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12542","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4929744476a8853c6be07209ff96983926c8ae552efd7b1da04c120d4108807","sha256:9da1d9ed8918715e8488243628873738a2fc39ad153777213cc535576465e9b4"],"state_sha256":"bd9296a4163342888e7ceb2be03ee76a108a156900b377137942e6b662cea69e"}