{"id":"W2135486194","doi":"10.1109/lics.2006.19","title":"Conditional Lower Bound for a System of Constant-Depth Proofs with Modular Connectives","year":2006,"lang":"en","type":"article","venue":"","topic":"Formal Methods in Verification","field":"Computer Science","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematical proof; Proof complexity; Constant (computer programming); Upper and lower bounds; Sequent calculus; Mathematics; Hierarchy; Modular design; Sequent; Exponential function; Discrete mathematics; Propositional calculus; Combinatorics; Calculus (dental); Computer science; Geometry","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003183483,0.00009007969,0.0001468219,0.00006294908,0.00007316428,0.0000497265,0.0002651027,0.00003879142,0.000005080689],"category_scores_gemma":[0.00002244106,0.00006882317,0.00003797801,0.000163763,0.0001386826,0.0003760256,0.00002867383,0.00003433118,0.000003289749],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005183213,"about_ca_system_score_gemma":0.00009371922,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001799913,"about_ca_topic_score_gemma":0.000007037037,"domain_scores_codex":[0.9991414,0.00004648524,0.0002173573,0.0002373752,0.0002071514,0.0001502307],"domain_scores_gemma":[0.9991593,0.0001096641,0.0001426336,0.0002948109,0.0002665757,0.00002702562],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00003109598,0.00005293368,0.0001673171,0.00006533842,0.00001413329,0.000001243037,0.00003032496,0.0004405838,0.002337044,0.9963627,0.0001082623,0.0003889973],"study_design_scores_gemma":[0.00260884,0.001291492,0.007979558,0.0001604122,0.00003252704,0.0001661746,0.0002857755,0.7231049,0.1826868,0.07845196,0.002685591,0.0005460338],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02220927,0.00003739157,0.9666449,0.00004553903,0.0001198915,0.0005128934,0.00001753334,0.000117957,0.01029462],"genre_scores_gemma":[0.5597301,1.231637e-7,0.4400715,0.00001433265,0.00001801003,0.00005541194,0.000004426358,0.000003921454,0.0001022241],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9179108,"threshold_uncertainty_score":0.2806527,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01706522866133151,"score_gpt":0.2603438644607698,"score_spread":0.2432786357994383,"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."}}