{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WO54QOFUVDYU5D7NJL5QDXF2HA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ce1d19613eb2995e7c1dbe9ae3b120c80c16384e88b5cc1a519aa0dddade940a","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-10T07:49:05Z","title_canon_sha256":"5462524d00f5c24e23510b67ba95f158ffe84e76c77dadf3cd785808bc7464de"},"schema_version":"1.0","source":{"id":"1509.03048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03048","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03048v1","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03048","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"WO54QOFUVDYU","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WO54QOFUVDYU5D7N","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WO54QOFU","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:43a1d9890d04850717b89eefde1fdcf614d5fce738dafc712c10c94c701420c7","target":"graph","created_at":"2026-05-18T01:11:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider sets $\\Gamma(n,s,k)$ of narrow clauses expressing that no definition of a size $s$ circuit with $n$ inputs is refutable in resolution R in $k$ steps. We show that every CNF shortly refutable in Extended R, ER, can be easily reduced to an instance of $\\Gamma(0,s,k)$ (with $s,k$ depending on the size of the ER-refutation) and, in particular, that $\\Gamma(0,s,k)$ when interpreted as a relativized NP search problem is complete among all such problems provably total in bounded arithmetic theory $V^1_1$.\n  We use the ideas of implicit proofs to define from $\\Gamma(0,s,k)$ a non-relativiz","authors_text":"Jan Krajicek","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-10T07:49:05Z","title":"Consistency of circuit evaluation, extended resolution and total NP search problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03048","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:739c705a77e72f5edd570ee8c61c1be9710aeeb7fe7490f2e14cf8058bdadff8","target":"record","created_at":"2026-05-18T01:11:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ce1d19613eb2995e7c1dbe9ae3b120c80c16384e88b5cc1a519aa0dddade940a","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-10T07:49:05Z","title_canon_sha256":"5462524d00f5c24e23510b67ba95f158ffe84e76c77dadf3cd785808bc7464de"},"schema_version":"1.0","source":{"id":"1509.03048","kind":"arxiv","version":1}},"canonical_sha256":"b3bbc838b4a8f14e8fed4afb01dcba381b5fde8421ffe680262a9d43b3f6f479","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3bbc838b4a8f14e8fed4afb01dcba381b5fde8421ffe680262a9d43b3f6f479","first_computed_at":"2026-05-18T01:11:55.056163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:55.056163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l+T9rUSWA9OA0V+og5nHo6dOY054sBb9vMOVwqjXEtQEW7ni0tIdrGa8QM5mbznGWVf8unIdadZbyl/VtYJDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:55.056559Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:739c705a77e72f5edd570ee8c61c1be9710aeeb7fe7490f2e14cf8058bdadff8","sha256:43a1d9890d04850717b89eefde1fdcf614d5fce738dafc712c10c94c701420c7"],"state_sha256":"3672a8b1103e979a67bc7657a23725172dcad87b85db3aad882a70453dd7fe0a"}