{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PYJOSAAKCQYKWXYF3OFWRDMHNC","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":"3c64d85c13dd04cec17d2c5888015754eed5b0f57815c9e1f02a62c2e091c974","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2011-06-15T15:19:01Z","title_canon_sha256":"b8ea98efd6a0fe0130f61be7c26c2229d1d2cd70ced859a4502906bd25da40be"},"schema_version":"1.0","source":{"id":"1106.2993","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2993","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2993v2","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2993","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"pith_short_12","alias_value":"PYJOSAAKCQYK","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PYJOSAAKCQYKWXYF","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PYJOSAAK","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:308654add7ab8980e3d7153de37871087d1128150f2ef27f6610f36466dec2f7","target":"graph","created_at":"2026-05-18T01:37:39Z","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 investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed sets K which have nonempty intersection with Q. We prove an effective version of Choquet's capacity theorem by showing that every computable capacity may be obtained from a computable measure in this way. We establish conditions on the measure m that characterize when the capacity of an m-random closed set equals zero. This includes new results in classical pro","authors_text":"Douglas Cenzer (University of Florida), Ferit Toska (University of Florida), Paul Brodhead (Indian River State College), Sebastian Wyman (University of Florida)","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2011-06-15T15:19:01Z","title":"Algorithmic Randomness and Capacity of Closed Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2993","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:a7aa7454a2b3152f93bbbed4961d889dba878d22987b80a982503e553414cac4","target":"record","created_at":"2026-05-18T01:37:39Z","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":"3c64d85c13dd04cec17d2c5888015754eed5b0f57815c9e1f02a62c2e091c974","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2011-06-15T15:19:01Z","title_canon_sha256":"b8ea98efd6a0fe0130f61be7c26c2229d1d2cd70ced859a4502906bd25da40be"},"schema_version":"1.0","source":{"id":"1106.2993","kind":"arxiv","version":2}},"canonical_sha256":"7e12e9000a1430ab5f05db8b688d8768ba5caa1b1fd2ebebe84dd92d3a03a230","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e12e9000a1430ab5f05db8b688d8768ba5caa1b1fd2ebebe84dd92d3a03a230","first_computed_at":"2026-05-18T01:37:39.413151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:39.413151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"frVoJiccLpySuyB5Tr3GWyoVXnZqUlucx9kB5YufpOp2OWgt6inIBHPgZitJIAY2EcZNweVAm18raMl5RAyfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:39.413746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2993","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7aa7454a2b3152f93bbbed4961d889dba878d22987b80a982503e553414cac4","sha256:308654add7ab8980e3d7153de37871087d1128150f2ef27f6610f36466dec2f7"],"state_sha256":"1a837c212445c99fd31f9d0f820e82ad4253a87f939446924276b8f8eae9838b"}