{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FAL7AFG3XGATXSU6QA6U77A7YO","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":"e8ece4e136ebe32feabf5b6952fb118f85bf3b92ca9098754b6a6134ebd9941d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-10T00:46:04Z","title_canon_sha256":"1f04df6c7309ec994fe8a4752b23e3a866a963f79ef90a31049a6f7f0ee65163"},"schema_version":"1.0","source":{"id":"1408.2169","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2169","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2169v1","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2169","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"FAL7AFG3XGAT","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FAL7AFG3XGATXSU6","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FAL7AFG3","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:4aab50bf0481614fbba55689732fe9cc8f9b39e4f00e506ab40f2594944215b1","target":"graph","created_at":"2026-05-18T02:45:30Z","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 various results on effective numberings and Friedberg numberings of families related to algorithmic randomness. The family of all Martin-L\\\"of random left-computably enumerable reals has a Friedberg numbering, as does the family of all $\\Pi^0_1$ classes of positive measure. On the other hand, the $\\Pi^0_1$ classes contained in the Martin-L\\\"of random reals do not even have an effective numbering, nor do the left-c.e. reals satisfying a fixed randomness constant. For $\\Pi^0_1$ classes contained in the class of reals satisfying a fixed randomness constant, we prove that at least an effe","authors_text":"Bj{\\o}rn Kjos-Hanssen, Katie Brodhead","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-10T00:46:04Z","title":"Numberings and randomness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2169","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:e2988df7e35b6ed085514f9bb85c75fd434906f3daac094a03f6b6df3aaf4cfa","target":"record","created_at":"2026-05-18T02:45:30Z","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":"e8ece4e136ebe32feabf5b6952fb118f85bf3b92ca9098754b6a6134ebd9941d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-10T00:46:04Z","title_canon_sha256":"1f04df6c7309ec994fe8a4752b23e3a866a963f79ef90a31049a6f7f0ee65163"},"schema_version":"1.0","source":{"id":"1408.2169","kind":"arxiv","version":1}},"canonical_sha256":"2817f014dbb9813bca9e803d4ffc1fc3bb468f37d3f8ce641fa30636f189281a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2817f014dbb9813bca9e803d4ffc1fc3bb468f37d3f8ce641fa30636f189281a","first_computed_at":"2026-05-18T02:45:30.168392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:30.168392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bVPCnqTDVKOPptj7YxC1WJbaA4lk+oUp7mGgsx1FJdbnaGjwXtWMBmqE+ZEsoSSq7iLSdQ5bkhkPrk28hm/rCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:30.169047Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2169","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2988df7e35b6ed085514f9bb85c75fd434906f3daac094a03f6b6df3aaf4cfa","sha256:4aab50bf0481614fbba55689732fe9cc8f9b39e4f00e506ab40f2594944215b1"],"state_sha256":"95b5a1f9de87080676cd4ea8b95a8ca558d2715e6f0d42cc9bfc560637673597"}