{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:UQBMLX5NTGFYENCS23NVSVBYUO","short_pith_number":"pith:UQBMLX5N","schema_version":"1.0","canonical_sha256":"a402c5dfad998b823452d6db595438a3989a479925b229929c7267d49c47de2f","source":{"kind":"arxiv","id":"1109.6749","version":1},"attestation_state":"computed","paper":{"title":"Characterizing the strongly jump-traceable sets via randomness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andre Nies, Denis Hirschfeldt, Noam Greenberg","submitted_at":"2011-09-30T08:34:31Z","abstract_excerpt":"We show that if a set $A$ is computable from every superlow 1-random set, then $A$ is strongly jump-traceable. This theorem shows that the computably enumerable (c.e.) strongly jump-traceable sets are exactly the c.e.\\ sets computable from every superlow 1-random set.\n  We also prove the analogous result for superhighness: a c.e.\\ set is strongly jump-traceable if and only if it is computable from every superhigh 1-random set.\n  Finally, we show that for each cost function $c$ with the limit condition there is a 1-random $\\Delta^0_2$ set $Y$ such that every c.e.\\ set $A \\le_T Y$ obeys $c$. To "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1109.6749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-09-30T08:34:31Z","cross_cats_sorted":[],"title_canon_sha256":"be53897732d560113ec5a80650430be232903d7f4e59ac03c69bc24a64b5b580","abstract_canon_sha256":"6d7c24ece2fa7ab52a4ecc474e664d76535379c0b7626e309e1742f1177bd9c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:52.556172Z","signature_b64":"yDSQuortg2nSwUVcaDw+Y47KhKiz5kBPlfpb3YFI74vLdqKaqhKIMxYU++mGbpOJLlqx0EtUFJAVYcKkBh0zCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a402c5dfad998b823452d6db595438a3989a479925b229929c7267d49c47de2f","last_reissued_at":"2026-05-18T04:11:52.555500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:52.555500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizing the strongly jump-traceable sets via randomness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andre Nies, Denis Hirschfeldt, Noam Greenberg","submitted_at":"2011-09-30T08:34:31Z","abstract_excerpt":"We show that if a set $A$ is computable from every superlow 1-random set, then $A$ is strongly jump-traceable. This theorem shows that the computably enumerable (c.e.) strongly jump-traceable sets are exactly the c.e.\\ sets computable from every superlow 1-random set.\n  We also prove the analogous result for superhighness: a c.e.\\ set is strongly jump-traceable if and only if it is computable from every superhigh 1-random set.\n  Finally, we show that for each cost function $c$ with the limit condition there is a 1-random $\\Delta^0_2$ set $Y$ such that every c.e.\\ set $A \\le_T Y$ obeys $c$. To "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6749","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.6749","created_at":"2026-05-18T04:11:52.555609+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.6749v1","created_at":"2026-05-18T04:11:52.555609+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6749","created_at":"2026-05-18T04:11:52.555609+00:00"},{"alias_kind":"pith_short_12","alias_value":"UQBMLX5NTGFY","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"UQBMLX5NTGFYENCS","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"UQBMLX5N","created_at":"2026-05-18T12:26:42.757692+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UQBMLX5NTGFYENCS23NVSVBYUO","json":"https://pith.science/pith/UQBMLX5NTGFYENCS23NVSVBYUO.json","graph_json":"https://pith.science/api/pith-number/UQBMLX5NTGFYENCS23NVSVBYUO/graph.json","events_json":"https://pith.science/api/pith-number/UQBMLX5NTGFYENCS23NVSVBYUO/events.json","paper":"https://pith.science/paper/UQBMLX5N"},"agent_actions":{"view_html":"https://pith.science/pith/UQBMLX5NTGFYENCS23NVSVBYUO","download_json":"https://pith.science/pith/UQBMLX5NTGFYENCS23NVSVBYUO.json","view_paper":"https://pith.science/paper/UQBMLX5N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.6749&json=true","fetch_graph":"https://pith.science/api/pith-number/UQBMLX5NTGFYENCS23NVSVBYUO/graph.json","fetch_events":"https://pith.science/api/pith-number/UQBMLX5NTGFYENCS23NVSVBYUO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UQBMLX5NTGFYENCS23NVSVBYUO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UQBMLX5NTGFYENCS23NVSVBYUO/action/storage_attestation","attest_author":"https://pith.science/pith/UQBMLX5NTGFYENCS23NVSVBYUO/action/author_attestation","sign_citation":"https://pith.science/pith/UQBMLX5NTGFYENCS23NVSVBYUO/action/citation_signature","submit_replication":"https://pith.science/pith/UQBMLX5NTGFYENCS23NVSVBYUO/action/replication_record"}},"created_at":"2026-05-18T04:11:52.555609+00:00","updated_at":"2026-05-18T04:11:52.555609+00:00"}