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We prove that every nonempty Pi^0_1 class contains a member which is not relatively c.e. and that every 1-generic real is relatively simple and above."},"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":"0705.0776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2007-05-06T01:59:43Z","cross_cats_sorted":[],"title_canon_sha256":"2e282e6878ae60241ffd5e7db303068449a6ecb28054aa2f7bd730bbbe6ee3ab","abstract_canon_sha256":"226d492356d8e4cbdfffeff96973ee76178545bb0bd440b57abc4756e45922fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:13.510114Z","signature_b64":"lbhywWMSuMjzJc6aeB7qyf6nA7eb05WuYR1ZLfzcQrkz8wMPyyBsrbqofwySub0okaAEcLZJE51VkFiCnzecAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d1744274743fb6da1f62375859450d8f9a0acd5b282489916a51fb50755c936","last_reissued_at":"2026-05-18T04:20:13.509435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:13.509435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relatively computably enumerable reals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Bernard A. 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We prove that every nonempty Pi^0_1 class contains a member which is not relatively c.e. and that every 1-generic real is relatively simple and above."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.0776","kind":"arxiv","version":2},"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":"0705.0776","created_at":"2026-05-18T04:20:13.509535+00:00"},{"alias_kind":"arxiv_version","alias_value":"0705.0776v2","created_at":"2026-05-18T04:20:13.509535+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.0776","created_at":"2026-05-18T04:20:13.509535+00:00"},{"alias_kind":"pith_short_12","alias_value":"LULUIJ2HIP5W","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"LULUIJ2HIP5W3IPW","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"LULUIJ2H","created_at":"2026-05-18T12:25:55.427421+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/LULUIJ2HIP5W3IPWEN2YLFCQ3D","json":"https://pith.science/pith/LULUIJ2HIP5W3IPWEN2YLFCQ3D.json","graph_json":"https://pith.science/api/pith-number/LULUIJ2HIP5W3IPWEN2YLFCQ3D/graph.json","events_json":"https://pith.science/api/pith-number/LULUIJ2HIP5W3IPWEN2YLFCQ3D/events.json","paper":"https://pith.science/paper/LULUIJ2H"},"agent_actions":{"view_html":"https://pith.science/pith/LULUIJ2HIP5W3IPWEN2YLFCQ3D","download_json":"https://pith.science/pith/LULUIJ2HIP5W3IPWEN2YLFCQ3D.json","view_paper":"https://pith.science/paper/LULUIJ2H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0705.0776&json=true","fetch_graph":"https://pith.science/api/pith-number/LULUIJ2HIP5W3IPWEN2YLFCQ3D/graph.json","fetch_events":"https://pith.science/api/pith-number/LULUIJ2HIP5W3IPWEN2YLFCQ3D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LULUIJ2HIP5W3IPWEN2YLFCQ3D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LULUIJ2HIP5W3IPWEN2YLFCQ3D/action/storage_attestation","attest_author":"https://pith.science/pith/LULUIJ2HIP5W3IPWEN2YLFCQ3D/action/author_attestation","sign_citation":"https://pith.science/pith/LULUIJ2HIP5W3IPWEN2YLFCQ3D/action/citation_signature","submit_replication":"https://pith.science/pith/LULUIJ2HIP5W3IPWEN2YLFCQ3D/action/replication_record"}},"created_at":"2026-05-18T04:20:13.509535+00:00","updated_at":"2026-05-18T04:20:13.509535+00:00"}