{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WYPDFGGXSGRENYBMKPMYFZTB4O","short_pith_number":"pith:WYPDFGGX","canonical_record":{"source":{"id":"1710.00422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-01T21:52:53Z","cross_cats_sorted":[],"title_canon_sha256":"32110c97ef05b6b8f518ea87fbcf2655f23b42d0cc7274e1a30b5af5dfcdbffc","abstract_canon_sha256":"66610e87e4c4fdf20f26fb0a036af8984beed1fdbee4e451753fb3014de95279"},"schema_version":"1.0"},"canonical_sha256":"b61e3298d791a246e02c53d982e661e3b9896f09fa8378a08c195cb8417b853a","source":{"kind":"arxiv","id":"1710.00422","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00422","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00422v1","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00422","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"pith_short_12","alias_value":"WYPDFGGXSGRE","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WYPDFGGXSGRENYBM","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WYPDFGGX","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WYPDFGGXSGRENYBMKPMYFZTB4O","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-01T21:52:53Z","cross_cats_sorted":[],"title_canon_sha256":"32110c97ef05b6b8f518ea87fbcf2655f23b42d0cc7274e1a30b5af5dfcdbffc","abstract_canon_sha256":"66610e87e4c4fdf20f26fb0a036af8984beed1fdbee4e451753fb3014de95279"},"schema_version":"1.0"},"canonical_sha256":"b61e3298d791a246e02c53d982e661e3b9896f09fa8378a08c195cb8417b853a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:44.256995Z","signature_b64":"HMe4WoGvQfjldEBPMahAM/gADLPdo9D60lfVWcBnYfv3lyiIpTso1SPQGWtBScO9SHFBUugQTLxFQ9vG6fG1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b61e3298d791a246e02c53d982e661e3b9896f09fa8378a08c195cb8417b853a","last_reissued_at":"2026-05-17T23:49:44.256485Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:44.256485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00422","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s1gUBk95SoTPD9LwWh27QIHMOPZLwKKzNkaERFJ3j41osyJ6PTDDOJbuySQa/Bj0U9TCOAgkQ1xLY+fb4g8sBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:47:15.899977Z"},"content_sha256":"a13e3cfc076473de19df5485d95d1418658e5d8d40f9fe7d4adb61b58da53b85","schema_version":"1.0","event_id":"sha256:a13e3cfc076473de19df5485d95d1418658e5d8d40f9fe7d4adb61b58da53b85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WYPDFGGXSGRENYBMKPMYFZTB4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Henkin constructions of models with size continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"John T. Baldwin, Michael C. Laskowski","submitted_at":"2017-10-01T21:52:53Z","abstract_excerpt":"We survey the technique of constructing customized models of size continuum in omega steps and illustrate the method by giving new proofs of mostly old results within this rubric. One new theorem, which is joint with Saharon Shelah, is that a pseudominimal theory has an atomic model of size continuum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00422","kind":"arxiv","version":1},"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":"2026-05-17T23:49:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PqzBgNytEDTLUCm8bdmeVCDqjZgkJ22ojlQjZovF+0i4LH/O/GvnQlZoNPYp+zfYJ3ZQtIbc8tyNP6pmnLOkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:47:15.900334Z"},"content_sha256":"60658f8a3b8df905284de23dea74a0ece2b4722753c2cd1241cb1749784ed06e","schema_version":"1.0","event_id":"sha256:60658f8a3b8df905284de23dea74a0ece2b4722753c2cd1241cb1749784ed06e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WYPDFGGXSGRENYBMKPMYFZTB4O/bundle.json","state_url":"https://pith.science/pith/WYPDFGGXSGRENYBMKPMYFZTB4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WYPDFGGXSGRENYBMKPMYFZTB4O/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":"2026-05-30T10:47:15Z","links":{"resolver":"https://pith.science/pith/WYPDFGGXSGRENYBMKPMYFZTB4O","bundle":"https://pith.science/pith/WYPDFGGXSGRENYBMKPMYFZTB4O/bundle.json","state":"https://pith.science/pith/WYPDFGGXSGRENYBMKPMYFZTB4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WYPDFGGXSGRENYBMKPMYFZTB4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WYPDFGGXSGRENYBMKPMYFZTB4O","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":"66610e87e4c4fdf20f26fb0a036af8984beed1fdbee4e451753fb3014de95279","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-01T21:52:53Z","title_canon_sha256":"32110c97ef05b6b8f518ea87fbcf2655f23b42d0cc7274e1a30b5af5dfcdbffc"},"schema_version":"1.0","source":{"id":"1710.00422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00422","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00422v1","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00422","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"pith_short_12","alias_value":"WYPDFGGXSGRE","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WYPDFGGXSGRENYBM","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WYPDFGGX","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:60658f8a3b8df905284de23dea74a0ece2b4722753c2cd1241cb1749784ed06e","target":"graph","created_at":"2026-05-17T23:49:44Z","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 survey the technique of constructing customized models of size continuum in omega steps and illustrate the method by giving new proofs of mostly old results within this rubric. One new theorem, which is joint with Saharon Shelah, is that a pseudominimal theory has an atomic model of size continuum.","authors_text":"John T. Baldwin, Michael C. Laskowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-01T21:52:53Z","title":"Henkin constructions of models with size continuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00422","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:a13e3cfc076473de19df5485d95d1418658e5d8d40f9fe7d4adb61b58da53b85","target":"record","created_at":"2026-05-17T23:49:44Z","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":"66610e87e4c4fdf20f26fb0a036af8984beed1fdbee4e451753fb3014de95279","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-01T21:52:53Z","title_canon_sha256":"32110c97ef05b6b8f518ea87fbcf2655f23b42d0cc7274e1a30b5af5dfcdbffc"},"schema_version":"1.0","source":{"id":"1710.00422","kind":"arxiv","version":1}},"canonical_sha256":"b61e3298d791a246e02c53d982e661e3b9896f09fa8378a08c195cb8417b853a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b61e3298d791a246e02c53d982e661e3b9896f09fa8378a08c195cb8417b853a","first_computed_at":"2026-05-17T23:49:44.256485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:44.256485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HMe4WoGvQfjldEBPMahAM/gADLPdo9D60lfVWcBnYfv3lyiIpTso1SPQGWtBScO9SHFBUugQTLxFQ9vG6fG1Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:44.256995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a13e3cfc076473de19df5485d95d1418658e5d8d40f9fe7d4adb61b58da53b85","sha256:60658f8a3b8df905284de23dea74a0ece2b4722753c2cd1241cb1749784ed06e"],"state_sha256":"0d443e355e205cfdf3d81cb41ae0f52dece6ce18e3683869682b38943a0cdfbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ho/fgAdThc7CTmGbh3r8ryRfD7xs/1xLynFNxlrgInFn+V6Mm+AZ+MebD9G46pG4TU4Cf4Jq3dGgvh+mowjqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:47:15.902217Z","bundle_sha256":"20a9373a7c91c4bb367b4afb8418bbf4fa496004a5a95da7b91324f56999be4c"}}