{"id":"W1532021344","doi":"10.1007/11538363_26","title":"Closure Properties of Weak Systems of Bounded Arithmetic","year":2005,"lang":"en","type":"book-chapter","venue":"Lecture notes in computer science","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Bounded function; Class (philosophy); Axiom; Complexity class; Closure (psychology); Discrete mathematics; Descriptive complexity theory; Second-order arithmetic; Computer science; Arithmetic; Mathematics; Algebra over a field; Time complexity; Pure mathematics; Artificial intelligence","routes":{"ca_aff":true,"ca_fund":false,"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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001465944,0.0004726375,0.0008786324,0.001335472,0.0001370542,0.0002126765,0.004691912,0.0003043587,0.000007592129],"category_scores_gemma":[0.0001580781,0.0003896677,0.0001826856,0.000988211,0.002305974,0.0006082914,0.001475739,0.0007793196,0.00001204982],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002020185,"about_ca_system_score_gemma":0.000766847,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003163957,"about_ca_topic_score_gemma":0.00003423755,"domain_scores_codex":[0.995409,0.00009398923,0.0008781779,0.001202323,0.001744846,0.0006716576],"domain_scores_gemma":[0.9963129,0.0003632045,0.0005538675,0.00191848,0.0007042778,0.0001473239],"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":[0.00005245619,0.0001448284,0.0002532679,0.0009079044,0.00007103159,0.00004443797,0.001597021,0.09684461,0.00730127,0.5362927,0.00001158294,0.3564789],"study_design_scores_gemma":[0.0009909652,0.00103029,0.000152561,0.004558185,0.00002856674,0.0002332937,0.000002242927,0.5048929,0.0581876,0.4258226,0.002456849,0.001643941],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0007988022,0.004143974,0.9908205,0.0001843172,0.0008740315,0.000626403,0.000006866584,0.00008013692,0.002464948],"genre_scores_gemma":[0.8012864,0.0001147962,0.1972934,0.0000871545,0.0002602042,0.00001535286,0.000001281914,0.0000440417,0.0008973737],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8004876,"threshold_uncertainty_score":0.9998555,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02784050416471322,"score_gpt":0.2617839800224799,"score_spread":0.2339434758577666,"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."}}