{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VU7DK2NETXVKX6HDQNRDMWFINM","short_pith_number":"pith:VU7DK2NE","schema_version":"1.0","canonical_sha256":"ad3e3569a49deaabf8e383623658a86b15a08e9025b8756382525c76a21fc051","source":{"kind":"arxiv","id":"1401.3823","version":2},"attestation_state":"computed","paper":{"title":"Comparing the strength of diagonally non-recursive functions in the absence of $\\Sigma^0_2$ induction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Fran\\c{c}ois G. Dorais, Jeffry L. Hirst, Paul Shafer","submitted_at":"2014-01-16T03:51:05Z","abstract_excerpt":"We prove that the statement \"there is a $k$ such that for every $f$ there is a $k$-bounded diagonally non-recursive function relative to $f$\" does not imply weak K\\\"onig's lemma over $\\mathrm{RCA}_0 + \\mathrm{B}\\Sigma^0_2$. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that every $k$-bounded diagonally non-recursive function computes a $2$-bounded diagonally non-recursive function may fail in the absence of $\\mathrm{I}\\Sigma^0_2$."},"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":"1401.3823","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-01-16T03:51:05Z","cross_cats_sorted":[],"title_canon_sha256":"6078110c32000ba513e33f66e620a15165c89984e72a73912e92aa00ad5879a4","abstract_canon_sha256":"e2133bc1808f9371ce4e01783ed02bfbfdc675de8495746693f21e1c6e20a005"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:29.421032Z","signature_b64":"7IhFyN+zq9M9td1g22ZAH37KH354Tr1nqwRt7P2DASOo4IhOnDgJE7QCG00YCTvo7YJrrjThxCbTtWaHWt98Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad3e3569a49deaabf8e383623658a86b15a08e9025b8756382525c76a21fc051","last_reissued_at":"2026-05-18T02:27:29.420265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:29.420265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparing the strength of diagonally non-recursive functions in the absence of $\\Sigma^0_2$ induction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Fran\\c{c}ois G. Dorais, Jeffry L. Hirst, Paul Shafer","submitted_at":"2014-01-16T03:51:05Z","abstract_excerpt":"We prove that the statement \"there is a $k$ such that for every $f$ there is a $k$-bounded diagonally non-recursive function relative to $f$\" does not imply weak K\\\"onig's lemma over $\\mathrm{RCA}_0 + \\mathrm{B}\\Sigma^0_2$. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that every $k$-bounded diagonally non-recursive function computes a $2$-bounded diagonally non-recursive function may fail in the absence of $\\mathrm{I}\\Sigma^0_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3823","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":"1401.3823","created_at":"2026-05-18T02:27:29.420420+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.3823v2","created_at":"2026-05-18T02:27:29.420420+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3823","created_at":"2026-05-18T02:27:29.420420+00:00"},{"alias_kind":"pith_short_12","alias_value":"VU7DK2NETXVK","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"VU7DK2NETXVKX6HD","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"VU7DK2NE","created_at":"2026-05-18T12:28:54.890064+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/VU7DK2NETXVKX6HDQNRDMWFINM","json":"https://pith.science/pith/VU7DK2NETXVKX6HDQNRDMWFINM.json","graph_json":"https://pith.science/api/pith-number/VU7DK2NETXVKX6HDQNRDMWFINM/graph.json","events_json":"https://pith.science/api/pith-number/VU7DK2NETXVKX6HDQNRDMWFINM/events.json","paper":"https://pith.science/paper/VU7DK2NE"},"agent_actions":{"view_html":"https://pith.science/pith/VU7DK2NETXVKX6HDQNRDMWFINM","download_json":"https://pith.science/pith/VU7DK2NETXVKX6HDQNRDMWFINM.json","view_paper":"https://pith.science/paper/VU7DK2NE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.3823&json=true","fetch_graph":"https://pith.science/api/pith-number/VU7DK2NETXVKX6HDQNRDMWFINM/graph.json","fetch_events":"https://pith.science/api/pith-number/VU7DK2NETXVKX6HDQNRDMWFINM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VU7DK2NETXVKX6HDQNRDMWFINM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VU7DK2NETXVKX6HDQNRDMWFINM/action/storage_attestation","attest_author":"https://pith.science/pith/VU7DK2NETXVKX6HDQNRDMWFINM/action/author_attestation","sign_citation":"https://pith.science/pith/VU7DK2NETXVKX6HDQNRDMWFINM/action/citation_signature","submit_replication":"https://pith.science/pith/VU7DK2NETXVKX6HDQNRDMWFINM/action/replication_record"}},"created_at":"2026-05-18T02:27:29.420420+00:00","updated_at":"2026-05-18T02:27:29.420420+00:00"}