{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:HH3NSGZEDPETYI7TWUYSTQCU5L","short_pith_number":"pith:HH3NSGZE","schema_version":"1.0","canonical_sha256":"39f6d91b241bc93c23f3b53129c054eacfd8ee834a36757bb8c4a3c6dabbe036","source":{"kind":"arxiv","id":"1902.03399","version":1},"attestation_state":"computed","paper":{"title":"Approximation of subsets of natural numbers by c.e. sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Farzad Didehvar, Mohsen Mansouri","submitted_at":"2019-02-09T10:11:23Z","abstract_excerpt":"The approximation of natural numbers subsets has always been one of the fundamental issues in computability theory. Computable approximation, $\\Delta_2$-approximation, as well as introducing the generically computable sets have been some efforts for this purpose. In this paper, a type of approximation for natural numbers subsets by computably enumerable sets will be examined. For an infinite and non-c.e set, $W_i$ will be an $A$.maximal (maximal inside $A$) if $W_i \\subseteq A$, is infinite and $\\forall j (W_i \\subseteq W_j \\subseteq A) \\to \\Delta (W_i, W_j )< \\infty$, where $\\Delta$ is the sy"},"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":"1902.03399","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-02-09T10:11:23Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"8bfa465a36740745373961788a3fe78b214ddea7a7a24a58c4b13fe63a52d31c","abstract_canon_sha256":"728cf609e9a44b2ba2b354764607bad79df219afb3bdf1c339ec88bdd89336c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:20.973890Z","signature_b64":"ulbL92QULWwEQUHX1lF+1LNN2/L+O9h9jHtLUOEGgs3WSRKRKHvj0RPhcb6LN6nAPc26zOrbkAwaMLoz6ztOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39f6d91b241bc93c23f3b53129c054eacfd8ee834a36757bb8c4a3c6dabbe036","last_reissued_at":"2026-05-17T23:54:20.973205Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:20.973205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximation of subsets of natural numbers by c.e. sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Farzad Didehvar, Mohsen Mansouri","submitted_at":"2019-02-09T10:11:23Z","abstract_excerpt":"The approximation of natural numbers subsets has always been one of the fundamental issues in computability theory. Computable approximation, $\\Delta_2$-approximation, as well as introducing the generically computable sets have been some efforts for this purpose. In this paper, a type of approximation for natural numbers subsets by computably enumerable sets will be examined. For an infinite and non-c.e set, $W_i$ will be an $A$.maximal (maximal inside $A$) if $W_i \\subseteq A$, is infinite and $\\forall j (W_i \\subseteq W_j \\subseteq A) \\to \\Delta (W_i, W_j )< \\infty$, where $\\Delta$ is the sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03399","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":"1902.03399","created_at":"2026-05-17T23:54:20.973333+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.03399v1","created_at":"2026-05-17T23:54:20.973333+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03399","created_at":"2026-05-17T23:54:20.973333+00:00"},{"alias_kind":"pith_short_12","alias_value":"HH3NSGZEDPET","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"HH3NSGZEDPETYI7T","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"HH3NSGZE","created_at":"2026-05-18T12:33:18.533446+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/HH3NSGZEDPETYI7TWUYSTQCU5L","json":"https://pith.science/pith/HH3NSGZEDPETYI7TWUYSTQCU5L.json","graph_json":"https://pith.science/api/pith-number/HH3NSGZEDPETYI7TWUYSTQCU5L/graph.json","events_json":"https://pith.science/api/pith-number/HH3NSGZEDPETYI7TWUYSTQCU5L/events.json","paper":"https://pith.science/paper/HH3NSGZE"},"agent_actions":{"view_html":"https://pith.science/pith/HH3NSGZEDPETYI7TWUYSTQCU5L","download_json":"https://pith.science/pith/HH3NSGZEDPETYI7TWUYSTQCU5L.json","view_paper":"https://pith.science/paper/HH3NSGZE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.03399&json=true","fetch_graph":"https://pith.science/api/pith-number/HH3NSGZEDPETYI7TWUYSTQCU5L/graph.json","fetch_events":"https://pith.science/api/pith-number/HH3NSGZEDPETYI7TWUYSTQCU5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HH3NSGZEDPETYI7TWUYSTQCU5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HH3NSGZEDPETYI7TWUYSTQCU5L/action/storage_attestation","attest_author":"https://pith.science/pith/HH3NSGZEDPETYI7TWUYSTQCU5L/action/author_attestation","sign_citation":"https://pith.science/pith/HH3NSGZEDPETYI7TWUYSTQCU5L/action/citation_signature","submit_replication":"https://pith.science/pith/HH3NSGZEDPETYI7TWUYSTQCU5L/action/replication_record"}},"created_at":"2026-05-17T23:54:20.973333+00:00","updated_at":"2026-05-17T23:54:20.973333+00:00"}