{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GXJAESPLW35YFLVGA4ZGEWMBMS","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":"b9035e51c5e92c3b8e1bc7d33f669c0b96f081e658101749f30114b1fc7831bb","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-08T13:23:20Z","title_canon_sha256":"55dd1548d17852242177a30600c0557d5a594ee92d06efd454381f27f234b904"},"schema_version":"1.0","source":{"id":"1212.1789","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1789","created_at":"2026-05-18T01:16:27Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1789v2","created_at":"2026-05-18T01:16:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1789","created_at":"2026-05-18T01:16:27Z"},{"alias_kind":"pith_short_12","alias_value":"GXJAESPLW35Y","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GXJAESPLW35YFLVG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GXJAESPL","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:8a977834de35a77908ddfbfcc9ce28d1c3d3d5f19fdca73d2296bdff8ac1988d","target":"graph","created_at":"2026-05-18T01:16:27Z","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":"It is well-known (cf. K.-Pudl\\'ak 1989) that a polynomial time algorithm finding tautologies hard for a propositional proof system $P$ exists iff $P$ is not optimal. Such an algorithm takes $1^{(k)}$ and outputs a tautology $\\tau_k$ of size at least $k$ such that $P$ is not p-bounded on the set of all $\\tau_k$'s.\n  We consider two more general search problems involving finding a hard formula, {\\bf Cert} and {\\bf Find}, motivated by two hypothetical situations: that one can prove that $\\np \\neq co\\np$ and that no optimal proof system exists. In {\\bf Cert} one is asked to find a witness that a g","authors_text":"Jan Krajicek","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-08T13:23:20Z","title":"On the computational complexity of finding hard tautologies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1789","kind":"arxiv","version":2},"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":"sha256:6de89d1cc0d1048fd0af7870901c588220021e6d5a5c37a6ebcaedcd6bfc1584","target":"record","created_at":"2026-05-18T01:16:27Z","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":"b9035e51c5e92c3b8e1bc7d33f669c0b96f081e658101749f30114b1fc7831bb","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-08T13:23:20Z","title_canon_sha256":"55dd1548d17852242177a30600c0557d5a594ee92d06efd454381f27f234b904"},"schema_version":"1.0","source":{"id":"1212.1789","kind":"arxiv","version":2}},"canonical_sha256":"35d20249ebb6fb82aea6073262598164b065ef7bf5fbd877c44790cf1bf2bd4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35d20249ebb6fb82aea6073262598164b065ef7bf5fbd877c44790cf1bf2bd4e","first_computed_at":"2026-05-18T01:16:27.961499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:27.961499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IGQni11MYw4rZgBqPsf4ilwEFzxEErFMokqgLlOvt3NI7+9Xlz4YyouUHIPpTLCafVv5AHW+4en+R6nbkrTNDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:27.961949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1789","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6de89d1cc0d1048fd0af7870901c588220021e6d5a5c37a6ebcaedcd6bfc1584","sha256:8a977834de35a77908ddfbfcc9ce28d1c3d3d5f19fdca73d2296bdff8ac1988d"],"state_sha256":"39fbb87faf1a94f0390ccc59f4e2939569ff604b3318db2c6a51e0432f4b316a"}