{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6WNWPARQ2CMYMCXJO2TZYLMLK6","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":"928cdaa6ce908993f32bc0fb480fe54d35eb27d8d34b9c2db2b9ef945b1baa8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-05-07T13:56:34Z","title_canon_sha256":"544238640b2ede83196fdbcaad337c7ad5929ae588de72b59ef26ad895c3015e"},"schema_version":"1.0","source":{"id":"1505.01707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01707","created_at":"2026-05-18T02:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01707v1","created_at":"2026-05-18T02:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01707","created_at":"2026-05-18T02:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"6WNWPARQ2CMY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6WNWPARQ2CMYMCXJ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6WNWPARQ","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:6baddf693526d71901a52734fb60c5018750b5cee453780ba704f0b8a7d71f6c","target":"graph","created_at":"2026-05-18T02:16:40Z","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 coarse description of a subset A of omega is a subset D of omega such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse descriptions of a given set A, especially when A is effectively random in some sense. We show that if A is 1-random and B is computable from every coarse description D of A, then B is K-trivial, which implies that if A is in fact weakly 2-random then B is computable. Our main tool is a kind of compactness theorem for cone-avoiding descriptions, which also all","authors_text":"Carl G. Jockusch Jr., Denis R. Hirschfeldt, Paul E. Schupp, Rutger Kuyper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-05-07T13:56:34Z","title":"Coarse Reducibility and Algorithmic Randomness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01707","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:a67e5436111716c13e09d957245988986c3c0b6281714c1d3cd32fdc1ac49a39","target":"record","created_at":"2026-05-18T02:16:40Z","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":"928cdaa6ce908993f32bc0fb480fe54d35eb27d8d34b9c2db2b9ef945b1baa8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-05-07T13:56:34Z","title_canon_sha256":"544238640b2ede83196fdbcaad337c7ad5929ae588de72b59ef26ad895c3015e"},"schema_version":"1.0","source":{"id":"1505.01707","kind":"arxiv","version":1}},"canonical_sha256":"f59b678230d099860ae976a79c2d8b57840d6c323a579ad4b3af6bf2484dc0de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f59b678230d099860ae976a79c2d8b57840d6c323a579ad4b3af6bf2484dc0de","first_computed_at":"2026-05-18T02:16:40.261048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:40.261048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GBZEaip8eSWqdivtlRDGu3udBQ0ZopwVLw9jIAn0PRvy9I4eltz2WkVCLYjMgqgR9Qm169yZqPCTBE8spg1AAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:40.261622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.01707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a67e5436111716c13e09d957245988986c3c0b6281714c1d3cd32fdc1ac49a39","sha256:6baddf693526d71901a52734fb60c5018750b5cee453780ba704f0b8a7d71f6c"],"state_sha256":"39057e6e8d3c26200cc1eb06e5acdadca897391f8ffd3edfb88d22ddac29d40b"}