{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7O3UN565DEXHBELYPHRUP6IOBU","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":"6914661ee973797b4f12d9d2bcb67124c3bde669fc1fd9d742af7117faa75f0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-30T15:18:08Z","title_canon_sha256":"9c38e1a397adb5eccfc30c808f47932a014e0a90ff142feeba018447d7956e54"},"schema_version":"1.0","source":{"id":"1409.8589","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8589","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8589v2","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8589","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"7O3UN565DEXH","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7O3UN565DEXHBELY","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7O3UN565","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:f0660ae60dcde7a51f2546ec02e7fa25d84e5918da4bc4a98003ee200cdf87d6","target":"graph","created_at":"2026-05-18T02:40:46Z","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":"A Martin-L\\\"of test $\\mathcal U$ is universal if it captures all non-Martin-L\\\"of random sequences, and it is optimal if for every ML-test $\\mathcal V$ there is a $c \\in \\omega$ such that $\\forall n(\\mathcal{V}_{n+c} \\subseteq \\mathcal{U}_n)$. We study the computational differences between universal and optimal ML-tests as well as the effects that these differences have on both the notion of layerwise computability and the Weihrauch degree of LAY, the function that produces a bound for a given Martin-L\\\"of random sequence's randomness deficiency. We prove several robustness and idempotence res","authors_text":"Paul Shafer, Rupert H\\\"olzl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-30T15:18:08Z","title":"Universality, optimality, and randomness deficiency"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8589","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":"sha256:79d662759083900a0ac139fc73728de0a022e9a5039c7303a5ad1c987eef9bc6","target":"record","created_at":"2026-05-18T02:40:46Z","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":"6914661ee973797b4f12d9d2bcb67124c3bde669fc1fd9d742af7117faa75f0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-30T15:18:08Z","title_canon_sha256":"9c38e1a397adb5eccfc30c808f47932a014e0a90ff142feeba018447d7956e54"},"schema_version":"1.0","source":{"id":"1409.8589","kind":"arxiv","version":2}},"canonical_sha256":"fbb746f7dd192e70917879e347f90e0d268e4e9ab0fee0db2cd4b98ce54cc5de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbb746f7dd192e70917879e347f90e0d268e4e9ab0fee0db2cd4b98ce54cc5de","first_computed_at":"2026-05-18T02:40:46.911128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:46.911128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yLnvPvndHOw4Jt08gvqud4FqmTbKopThkdIEMZEwxMtWE05gtfVYWKNsyeUVKZolHq2HiTI524Xzd/dVWWS4Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:46.911584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8589","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79d662759083900a0ac139fc73728de0a022e9a5039c7303a5ad1c987eef9bc6","sha256:f0660ae60dcde7a51f2546ec02e7fa25d84e5918da4bc4a98003ee200cdf87d6"],"state_sha256":"1e6b18f42842d15b9da50f4b898d7b09ad6ef6fc1cad4972b7ba9f904bb4bac8"}