{"id":"W2112512535","doi":"10.1145/1183278.1183283","title":"The strength of replacement in weak arithmetic","year":2006,"lang":"en","type":"article","venue":"ACM Transactions on Computational Logic","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":47,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Bounded function; Discrete mathematics; Class (philosophy); Axiom; Combinatorics; Complexity class; Polynomial; Integer (computer science); Quantifier (linguistics); Quantifier elimination; P; Time complexity; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.005928986,0.00069846,0.0009807377,0.002049627,0.002790669,0.005411325,0.002340744,0.001990756,0.004647048],"category_scores_gemma":[0.01194168,0.001341007,0.002333214,0.001286211,0.0128778,0.01235626,0.008455612,0.00640272,0.001003674],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00267965,"about_ca_system_score_gemma":0.001720695,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001784351,"about_ca_topic_score_gemma":0.001322794,"domain_scores_codex":[0.9915805,0.002201392,0.0008002331,0.001862593,0.002664104,0.0008910974],"domain_scores_gemma":[0.9880377,0.006236266,0.0006808648,0.002945702,0.001567919,0.0005315354],"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":[0.00004121478,0.000008597606,0.000522943,0.00007886894,0.00001891353,0.00005163673,0.0003065296,0.0006899486,0.001074281,0.9919696,0.000614743,0.004622628],"study_design_scores_gemma":[0.00003568919,0.0001078885,0.0005474772,0.00005846619,0.00005347898,0.0001700458,0.0002202965,0.007133517,0.004047414,0.9736022,0.0139841,0.00003935929],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2123943,0.002352469,0.6196578,0.006577998,0.0006512342,0.0001777835,0.0006726029,0.001738501,0.1557772],"genre_scores_gemma":[0.9149145,0.0005987988,0.07110613,0.001262552,0.0003991546,0.0001693449,0.0003593293,0.0001860149,0.01100418],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005928986,"threshold_uncertainty_score":0.03135592,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02121284245199038,"score_gpt":0.2584923929182951,"score_spread":0.2372795504663047,"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."}}