{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3IS5W2SAYVU7EGRAHV24MWKEIN","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":"48847ee9252c24ca1caeee3668bdea20bf40d207e19e289f8a72185996a669f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-29T20:46:18Z","title_canon_sha256":"e2ff07a4d6d72ab085bdbce8b458534b4134dc53cfc7995feb29216899342a26"},"schema_version":"1.0","source":{"id":"1304.7797","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7797","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7797v1","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7797","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"3IS5W2SAYVU7","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3IS5W2SAYVU7EGRA","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3IS5W2SA","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:5926ecdc65c46d4a6e4e2f0d1a06f70cf06eb8a4a77788173b8f46e180a60774","target":"graph","created_at":"2026-05-18T03:26:51Z","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":"The randomization of a complete first order theory T is the complete continuous theory T^R with two sorts, a sort for random elements of models of T, and a sort for events in an underlying probability space. We give necessary and sufficient conditions for an element to be definable over a set of parameters in a model of T^R.","authors_text":"H. Jerome Keisler, Isaac Goldbring, Uri Andrews","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-29T20:46:18Z","title":"Definable closure in randomizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7797","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:b2668a47d9ffccdf295dd6fd8a1f1b515714a16375cfba4508b523fae62dd2d2","target":"record","created_at":"2026-05-18T03:26:51Z","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":"48847ee9252c24ca1caeee3668bdea20bf40d207e19e289f8a72185996a669f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-29T20:46:18Z","title_canon_sha256":"e2ff07a4d6d72ab085bdbce8b458534b4134dc53cfc7995feb29216899342a26"},"schema_version":"1.0","source":{"id":"1304.7797","kind":"arxiv","version":1}},"canonical_sha256":"da25db6a40c569f21a203d75c65944434b954a73a204fa678821ae2dedaa785b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da25db6a40c569f21a203d75c65944434b954a73a204fa678821ae2dedaa785b","first_computed_at":"2026-05-18T03:26:51.840098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:51.840098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gY4kRPhgUOeWUTFxy2NIfkf0Torkl8f0BTaC9EmJZKI7Lg8rnZnWqD0NRF4xNGONqO0ypWKjC9g+cyLOUd51BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:51.840640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7797","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2668a47d9ffccdf295dd6fd8a1f1b515714a16375cfba4508b523fae62dd2d2","sha256:5926ecdc65c46d4a6e4e2f0d1a06f70cf06eb8a4a77788173b8f46e180a60774"],"state_sha256":"cd0e4ad329234b7579ec7f3d713d20c8517f435f229e449a1a2347b1de398578"}