{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3NXIUU72BNB5QB666LUE3ALBJQ","short_pith_number":"pith:3NXIUU72","schema_version":"1.0","canonical_sha256":"db6e8a53fa0b43d807def2e84d81614c141a5485a2396b0709f893cb29d47994","source":{"kind":"arxiv","id":"1411.3010","version":1},"attestation_state":"computed","paper":{"title":"Computational Complexity of Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Leonid A. Levin","submitted_at":"2014-11-11T22:50:51Z","abstract_excerpt":"Below is a translation from my Russian paper. I added references, unavailable to me in Moscow. Similar results have been also given in [Schnorr Stumpf 75] (see also [Lynch 75]). Earlier relevant work (classical theorems like Compression, Speed-up, etc.) was done in [Tseitin 56, Rabin 59, Hartmanis Stearns 65, Blum 67, Trakhtenbrot 67, Meyer Fischer 72].\n  I translated only the part with the statement of the results. Instead of the proof part I appended a later (1979, unpublished) proof sketch of a slightly tighter version. The improvement is based on the results of [Meyer Winklmann 78, Sipser "},"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":"1411.3010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-11-11T22:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"538571b105e4f7844f4385c02cfaa301efc42ffe70bdd446fca8969f4e9451d9","abstract_canon_sha256":"56c73290cde16f03bf68f3ed26797b843ed744168ad4a1dde114298aeea6fc40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:33.523801Z","signature_b64":"1qLP2L6blYpcuxSjfSvpm6nSiAxTi/h3O+Y8/6met9efb3Ze8iH8Zw0ZLSjOJh7r8iJ5nU3k3fVR9tOs81F1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db6e8a53fa0b43d807def2e84d81614c141a5485a2396b0709f893cb29d47994","last_reissued_at":"2026-05-17T23:59:33.523335Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:33.523335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computational Complexity of Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Leonid A. Levin","submitted_at":"2014-11-11T22:50:51Z","abstract_excerpt":"Below is a translation from my Russian paper. I added references, unavailable to me in Moscow. Similar results have been also given in [Schnorr Stumpf 75] (see also [Lynch 75]). Earlier relevant work (classical theorems like Compression, Speed-up, etc.) was done in [Tseitin 56, Rabin 59, Hartmanis Stearns 65, Blum 67, Trakhtenbrot 67, Meyer Fischer 72].\n  I translated only the part with the statement of the results. Instead of the proof part I appended a later (1979, unpublished) proof sketch of a slightly tighter version. The improvement is based on the results of [Meyer Winklmann 78, Sipser "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3010","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":"1411.3010","created_at":"2026-05-17T23:59:33.523402+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.3010v1","created_at":"2026-05-17T23:59:33.523402+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3010","created_at":"2026-05-17T23:59:33.523402+00:00"},{"alias_kind":"pith_short_12","alias_value":"3NXIUU72BNB5","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3NXIUU72BNB5QB66","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3NXIUU72","created_at":"2026-05-18T12:28:11.866339+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/3NXIUU72BNB5QB666LUE3ALBJQ","json":"https://pith.science/pith/3NXIUU72BNB5QB666LUE3ALBJQ.json","graph_json":"https://pith.science/api/pith-number/3NXIUU72BNB5QB666LUE3ALBJQ/graph.json","events_json":"https://pith.science/api/pith-number/3NXIUU72BNB5QB666LUE3ALBJQ/events.json","paper":"https://pith.science/paper/3NXIUU72"},"agent_actions":{"view_html":"https://pith.science/pith/3NXIUU72BNB5QB666LUE3ALBJQ","download_json":"https://pith.science/pith/3NXIUU72BNB5QB666LUE3ALBJQ.json","view_paper":"https://pith.science/paper/3NXIUU72","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.3010&json=true","fetch_graph":"https://pith.science/api/pith-number/3NXIUU72BNB5QB666LUE3ALBJQ/graph.json","fetch_events":"https://pith.science/api/pith-number/3NXIUU72BNB5QB666LUE3ALBJQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3NXIUU72BNB5QB666LUE3ALBJQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3NXIUU72BNB5QB666LUE3ALBJQ/action/storage_attestation","attest_author":"https://pith.science/pith/3NXIUU72BNB5QB666LUE3ALBJQ/action/author_attestation","sign_citation":"https://pith.science/pith/3NXIUU72BNB5QB666LUE3ALBJQ/action/citation_signature","submit_replication":"https://pith.science/pith/3NXIUU72BNB5QB666LUE3ALBJQ/action/replication_record"}},"created_at":"2026-05-17T23:59:33.523402+00:00","updated_at":"2026-05-17T23:59:33.523402+00:00"}