{"id":"W2397708339","doi":"10.4169/amer.math.monthly.118.10.921","title":"Chaotic Orderings of the Rationals and Reals","year":2011,"lang":"en","type":"article","venue":"American Mathematical Monthly","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Monotonic function; Rational number; Term (time); Mathematics; Set (abstract data type); Real number; Discrete mathematics; Arithmetic progression; Arithmetic; Chaotic; Combinatorics; Computer science; Artificial intelligence; Mathematical analysis; Physics","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":[],"consensus_categories":[],"category_scores_codex":[0.0004494903,0.0002000922,0.0005584063,0.00004867228,0.00007552458,0.00001709844,0.0003079959,0.000051799,0.0003697719],"category_scores_gemma":[0.001556788,0.0001239798,0.0001328129,0.000259504,0.0007326221,0.00007205846,0.0001756804,0.0001384389,0.00001995947],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000138602,"about_ca_system_score_gemma":0.0000246326,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000436791,"about_ca_topic_score_gemma":0.000009284051,"domain_scores_codex":[0.9984558,0.00007930455,0.0006252305,0.0002256923,0.000351383,0.0002625659],"domain_scores_gemma":[0.997887,0.000941198,0.0004053057,0.0005548853,0.00008953409,0.0001221361],"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":[0.00001028453,0.0002536681,0.0002893849,0.0002359465,0.00004727523,0.000001680252,0.001630196,3.488592e-7,0.0002650859,0.9965742,0.0001812692,0.0005106458],"study_design_scores_gemma":[0.0001415244,0.0000893666,0.003125768,0.0001219443,0.00006561469,0.00001055806,0.0003992469,0.002422441,0.0004588311,0.992952,0.000057292,0.0001554023],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6961017,0.00004586312,0.01797851,0.0007731728,0.00006102455,0.0008988057,0.00003502039,0.0001069745,0.283999],"genre_scores_gemma":[0.9342774,0.000007584357,0.06504904,0.0001486863,0.00001754491,0.00003813463,6.243897e-7,0.00003329119,0.0004277304],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2835712,"threshold_uncertainty_score":0.505575,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04261368746076361,"score_gpt":0.2742444422707364,"score_spread":0.2316307548099727,"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."}}