{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DW2HNQXPGVI3ST5HMRRX4F7FPZ","short_pith_number":"pith:DW2HNQXP","schema_version":"1.0","canonical_sha256":"1db476c2ef3551b94fa764637e17e57e5bb530568f25d7cab80ae187ef6bd604","source":{"kind":"arxiv","id":"1811.07172","version":1},"attestation_state":"computed","paper":{"title":"Dense computability, upper cones, and minimal pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Carl G. Jockusch Jr, Denis R. Hirschfeldt, Eric P. Astor","submitted_at":"2018-11-17T14:51:41Z","abstract_excerpt":"This paper concerns algorithms that give correct answers with (asymptotic) density $1$. A dense description of a function $g : \\omega \\to \\omega$ is a partial function $f$ on $\\omega$ such that $\\left\\{n : f(n) = g(n)\\right\\}$ has density $1$. We define $g$ to be densely computable if it has a partial computable dense description $f$. Several previous authors have studied the stronger notions of generic computability and coarse computability, which correspond respectively to requiring in addition that $g$ and $f$ agree on the domain of $f$, and to requiring that $f$ be total. Strengthening the"},"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":"1811.07172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-11-17T14:51:41Z","cross_cats_sorted":[],"title_canon_sha256":"64d6d8169b9c7b166dfe00fab8a88b74f71c23ac5d12a02a160fbba82f7dbf0d","abstract_canon_sha256":"4a954c19bf3a3718dfb98a89fb79e5142a0a82f96ad14e04cc417a34787cd1ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:28.725301Z","signature_b64":"tr1AF4zDs2vyw76bVFA9Gk/mryUaAjOiNrtYXQirkjakKECUaJclIVQN66N66+U1Ft7V4/7AzN9KPvNLoeYHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1db476c2ef3551b94fa764637e17e57e5bb530568f25d7cab80ae187ef6bd604","last_reissued_at":"2026-05-18T00:00:28.724697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:28.724697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dense computability, upper cones, and minimal pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Carl G. Jockusch Jr, Denis R. Hirschfeldt, Eric P. Astor","submitted_at":"2018-11-17T14:51:41Z","abstract_excerpt":"This paper concerns algorithms that give correct answers with (asymptotic) density $1$. A dense description of a function $g : \\omega \\to \\omega$ is a partial function $f$ on $\\omega$ such that $\\left\\{n : f(n) = g(n)\\right\\}$ has density $1$. We define $g$ to be densely computable if it has a partial computable dense description $f$. Several previous authors have studied the stronger notions of generic computability and coarse computability, which correspond respectively to requiring in addition that $g$ and $f$ agree on the domain of $f$, and to requiring that $f$ be total. Strengthening the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07172","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":"1811.07172","created_at":"2026-05-18T00:00:28.724788+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.07172v1","created_at":"2026-05-18T00:00:28.724788+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07172","created_at":"2026-05-18T00:00:28.724788+00:00"},{"alias_kind":"pith_short_12","alias_value":"DW2HNQXPGVI3","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DW2HNQXPGVI3ST5H","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DW2HNQXP","created_at":"2026-05-18T12:32:19.392346+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/DW2HNQXPGVI3ST5HMRRX4F7FPZ","json":"https://pith.science/pith/DW2HNQXPGVI3ST5HMRRX4F7FPZ.json","graph_json":"https://pith.science/api/pith-number/DW2HNQXPGVI3ST5HMRRX4F7FPZ/graph.json","events_json":"https://pith.science/api/pith-number/DW2HNQXPGVI3ST5HMRRX4F7FPZ/events.json","paper":"https://pith.science/paper/DW2HNQXP"},"agent_actions":{"view_html":"https://pith.science/pith/DW2HNQXPGVI3ST5HMRRX4F7FPZ","download_json":"https://pith.science/pith/DW2HNQXPGVI3ST5HMRRX4F7FPZ.json","view_paper":"https://pith.science/paper/DW2HNQXP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.07172&json=true","fetch_graph":"https://pith.science/api/pith-number/DW2HNQXPGVI3ST5HMRRX4F7FPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/DW2HNQXPGVI3ST5HMRRX4F7FPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DW2HNQXPGVI3ST5HMRRX4F7FPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DW2HNQXPGVI3ST5HMRRX4F7FPZ/action/storage_attestation","attest_author":"https://pith.science/pith/DW2HNQXPGVI3ST5HMRRX4F7FPZ/action/author_attestation","sign_citation":"https://pith.science/pith/DW2HNQXPGVI3ST5HMRRX4F7FPZ/action/citation_signature","submit_replication":"https://pith.science/pith/DW2HNQXPGVI3ST5HMRRX4F7FPZ/action/replication_record"}},"created_at":"2026-05-18T00:00:28.724788+00:00","updated_at":"2026-05-18T00:00:28.724788+00:00"}