{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:56TNFAZOC3OQ7IXFILO2LRCMEC","short_pith_number":"pith:56TNFAZO","canonical_record":{"source":{"id":"1810.12542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-30T06:25:41Z","cross_cats_sorted":[],"title_canon_sha256":"3a62457e7bc960c9e6fac43cd3b728176ff1e91e77d1785907f626d2637b355f","abstract_canon_sha256":"a6d9a2e7bae546409a2851a80f65bf7a89282fdd8b219c2e8c01d091acc3ed80"},"schema_version":"1.0"},"canonical_sha256":"efa6d2832e16dd0fa2e542dda5c44c20a3f9702c7a2931fad89286f928b38afe","source":{"kind":"arxiv","id":"1810.12542","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:56TNFAZOC3OQ7IXFILO2LRCMEC","target":"record","payload":{"canonical_record":{"source":{"id":"1810.12542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-30T06:25:41Z","cross_cats_sorted":[],"title_canon_sha256":"3a62457e7bc960c9e6fac43cd3b728176ff1e91e77d1785907f626d2637b355f","abstract_canon_sha256":"a6d9a2e7bae546409a2851a80f65bf7a89282fdd8b219c2e8c01d091acc3ed80"},"schema_version":"1.0"},"canonical_sha256":"efa6d2832e16dd0fa2e542dda5c44c20a3f9702c7a2931fad89286f928b38afe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:06.585714Z","signature_b64":"eKaXp5a5dglrTTx+gqC/efL7lLwFsvGa44BDl1prEnVfuyJcqPxFwfz+jBtfrEfV9jhFdrpxMSnTw2DYZ9fmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efa6d2832e16dd0fa2e542dda5c44c20a3f9702c7a2931fad89286f928b38afe","last_reissued_at":"2026-05-18T00:01:06.585255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:06.585255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.12542","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2GqEwM95nQF/trd4JCA1QD3DALHIcNtJOLqeHVHmwR7CuN4ssyahzp7qkG+8rvlqFNopDNu6HuWqFgx3cHWKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T18:53:56.063654Z"},"content_sha256":"c4929744476a8853c6be07209ff96983926c8ae552efd7b1da04c120d4108807","schema_version":"1.0","event_id":"sha256:c4929744476a8853c6be07209ff96983926c8ae552efd7b1da04c120d4108807"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:56TNFAZOC3OQ7IXFILO2LRCMEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Harrington's model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Vassily Lyubetsky, Vladimir Kanovei","submitted_at":"2018-10-30T06:25:41Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12542","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UVa3XgHsIAO1Akl6AEFtyAQMsNkziWRhOkPy8keTGu9EsC+jR24gYZBy/cwwAxDJo2RWJrInblGPs7CwUZlhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T18:53:56.064002Z"},"content_sha256":"9da1d9ed8918715e8488243628873738a2fc39ad153777213cc535576465e9b4","schema_version":"1.0","event_id":"sha256:9da1d9ed8918715e8488243628873738a2fc39ad153777213cc535576465e9b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/56TNFAZOC3OQ7IXFILO2LRCMEC/bundle.json","state_url":"https://pith.science/pith/56TNFAZOC3OQ7IXFILO2LRCMEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/56TNFAZOC3OQ7IXFILO2LRCMEC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-19T18:53:56Z","links":{"resolver":"https://pith.science/pith/56TNFAZOC3OQ7IXFILO2LRCMEC","bundle":"https://pith.science/pith/56TNFAZOC3OQ7IXFILO2LRCMEC/bundle.json","state":"https://pith.science/pith/56TNFAZOC3OQ7IXFILO2LRCMEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/56TNFAZOC3OQ7IXFILO2LRCMEC/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dONmdBh8Y3+a4bOIuQrFX1IekitzT544wP4XT8iGeZ5x06fGQx4UG0duMsFmtkwAgctFKilZ94nJ92ffWEaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T18:53:56.065958Z","bundle_sha256":"fb507d82109ad46cf12832a1683eb0522402fc22ea98ee5f774146b5a0ebcab8"}}