{"id":"W2767976260","doi":"10.1016/j.apal.2019.102735","title":"Feasibly constructive proofs of succinct weak circuit lower bounds","year":2019,"lang":"en","type":"article","venue":"Annals of Pure and Applied Logic","topic":"Computability, Logic, AI Algorithms","field":"Computer Science","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"European Research Council; Natural Sciences and Engineering Research Council of Canada; Austrian Science Fund; European Commission","keywords":"Mathematical proof; Mathematics; Pigeonhole principle; Upper and lower bounds; Proof complexity; Discrete mathematics; Bounded function; Combinatorics; Constructive; Logarithm; Computer science","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.007570582,0.003226498,0.002142134,0.002750503,0.002454196,0.008648285,0.006214592,0.003005289,0.02445405],"category_scores_gemma":[0.05831847,0.003164476,0.003755066,0.003261068,0.005964531,0.01770917,0.01101387,0.01330464,0.004108591],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004000288,"about_ca_system_score_gemma":0.003342971,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001173501,"about_ca_topic_score_gemma":0.00301733,"domain_scores_codex":[0.9878426,0.004769697,0.0006712208,0.001401867,0.004224575,0.001090076],"domain_scores_gemma":[0.8962344,0.08766724,0.001497738,0.009514568,0.004016296,0.001069634],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0004149233,0.0003069681,0.0005217711,0.0007510166,0.0001758398,0.0002379434,0.0006213732,0.0196539,0.003955376,0.9142445,0.01305568,0.04606054],"study_design_scores_gemma":[0.0001052812,0.00003407753,0.000107982,0.0001005008,0.00009819221,0.00007501253,0.00006872713,0.03328498,0.003829312,0.9566602,0.005604452,0.00003122884],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02675246,0.00121075,0.9121974,0.007939999,0.0007021958,0.0003926146,0.001698376,0.00337253,0.04573378],"genre_scores_gemma":[0.5727255,0.001747341,0.393173,0.004481355,0.001430479,0.001189126,0.003097537,0.002231768,0.01992395],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02445405,"threshold_uncertainty_score":0.08180696,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03561292216084491,"score_gpt":0.2667928805127758,"score_spread":0.2311799583519309,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}