{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:34FUKSAWJYTQOPWYVLRPHQ5Y2Z","short_pith_number":"pith:34FUKSAW","schema_version":"1.0","canonical_sha256":"df0b4548164e27073ed8aae2f3c3b8d6529cbb3e389ebe7da8b1064926a87b6d","source":{"kind":"arxiv","id":"1904.13191","version":1},"attestation_state":"computed","paper":{"title":"Case Study of the Proof of Cook's theorem - Interpretation of A(w)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Yu Li","submitted_at":"2019-04-30T12:34:20Z","abstract_excerpt":"Cook's theorem is commonly expressed such as any polynomial time-verifiable problem can be reduced to the SAT problem. The proof of Cook's theorem consists in constructing a propositional formula A(w) to simulate a computation of TM, and such A(w) is claimed to be CNF to represent a polynomial time-verifiable problem w. In this paper, we investigate A(w) through a very simple example and show that, A(w) has just an appearance of CNF, but not a true logical form. This case study suggests that there exists the begging the question in Cook's theorem."},"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":"1904.13191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-04-30T12:34:20Z","cross_cats_sorted":[],"title_canon_sha256":"59328ca53be8eb947535c31fb35105904535bfb65ec5a922f67f49eacb342f9d","abstract_canon_sha256":"97e1c0b6774544653d145c4e3090e5762789b72ebdd4d83ebb75fde7a4cb415e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:21.978994Z","signature_b64":"E35d7pZjbf8iIIPEVKaY8+6GWgw1HMZ/5M2g+LiT4yoY+N0GE2izuaAgnHsUwi+d+cXQzKUkE/2CH61jOSwkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df0b4548164e27073ed8aae2f3c3b8d6529cbb3e389ebe7da8b1064926a87b6d","last_reissued_at":"2026-05-17T23:47:21.978586Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:21.978586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Case Study of the Proof of Cook's theorem - Interpretation of A(w)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Yu Li","submitted_at":"2019-04-30T12:34:20Z","abstract_excerpt":"Cook's theorem is commonly expressed such as any polynomial time-verifiable problem can be reduced to the SAT problem. The proof of Cook's theorem consists in constructing a propositional formula A(w) to simulate a computation of TM, and such A(w) is claimed to be CNF to represent a polynomial time-verifiable problem w. In this paper, we investigate A(w) through a very simple example and show that, A(w) has just an appearance of CNF, but not a true logical form. This case study suggests that there exists the begging the question in Cook's theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.13191","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":"1904.13191","created_at":"2026-05-17T23:47:21.978644+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.13191v1","created_at":"2026-05-17T23:47:21.978644+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.13191","created_at":"2026-05-17T23:47:21.978644+00:00"},{"alias_kind":"pith_short_12","alias_value":"34FUKSAWJYTQ","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"34FUKSAWJYTQOPWY","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"34FUKSAW","created_at":"2026-05-18T12:33:07.085635+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/34FUKSAWJYTQOPWYVLRPHQ5Y2Z","json":"https://pith.science/pith/34FUKSAWJYTQOPWYVLRPHQ5Y2Z.json","graph_json":"https://pith.science/api/pith-number/34FUKSAWJYTQOPWYVLRPHQ5Y2Z/graph.json","events_json":"https://pith.science/api/pith-number/34FUKSAWJYTQOPWYVLRPHQ5Y2Z/events.json","paper":"https://pith.science/paper/34FUKSAW"},"agent_actions":{"view_html":"https://pith.science/pith/34FUKSAWJYTQOPWYVLRPHQ5Y2Z","download_json":"https://pith.science/pith/34FUKSAWJYTQOPWYVLRPHQ5Y2Z.json","view_paper":"https://pith.science/paper/34FUKSAW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.13191&json=true","fetch_graph":"https://pith.science/api/pith-number/34FUKSAWJYTQOPWYVLRPHQ5Y2Z/graph.json","fetch_events":"https://pith.science/api/pith-number/34FUKSAWJYTQOPWYVLRPHQ5Y2Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/34FUKSAWJYTQOPWYVLRPHQ5Y2Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/34FUKSAWJYTQOPWYVLRPHQ5Y2Z/action/storage_attestation","attest_author":"https://pith.science/pith/34FUKSAWJYTQOPWYVLRPHQ5Y2Z/action/author_attestation","sign_citation":"https://pith.science/pith/34FUKSAWJYTQOPWYVLRPHQ5Y2Z/action/citation_signature","submit_replication":"https://pith.science/pith/34FUKSAWJYTQOPWYVLRPHQ5Y2Z/action/replication_record"}},"created_at":"2026-05-17T23:47:21.978644+00:00","updated_at":"2026-05-17T23:47:21.978644+00:00"}