{"id":"W1978419161","doi":"10.5802/jtnb.596","title":"Power-free values, large deviations, and integer points on irrational curves","year":2008,"lang":"lv","type":"article","venue":"Journal de Théorie des Nombres de Bordeaux","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Irrational number; Combinatorics; Multiplicity (mathematics); Degree (music); Number theory; Integer (computer science); Entropy (arrow of time); Discrete mathematics; Mathematical analysis; Geometry; Physics; Quantum mechanics","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","sts","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.004694404,0.0005575182,0.0007375443,0.0004370692,0.001477795,0.0003463555,0.0009717663,0.0003447597,0.00246166],"category_scores_gemma":[0.007915449,0.0005131433,0.0003408956,0.0004890186,0.0006557648,0.0005912742,0.0004215675,0.001914218,0.0002923103],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001022252,"about_ca_system_score_gemma":0.001855718,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000246053,"about_ca_topic_score_gemma":0.00003496811,"domain_scores_codex":[0.9944622,0.001176112,0.001121442,0.0004854674,0.001408143,0.001346642],"domain_scores_gemma":[0.9948658,0.001943757,0.0005633843,0.0008638996,0.0008755483,0.0008876287],"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":[0.0008302593,0.001711945,0.04280987,0.0008725014,0.001126299,0.001617824,0.005763399,0.00002812084,0.0001464592,0.5220018,0.4227148,0.0003766623],"study_design_scores_gemma":[0.002830758,0.0007283688,0.02672116,0.001858915,0.0002599726,0.007112938,0.001421166,0.00168769,0.0001506305,0.9428096,0.01372304,0.0006957126],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8157655,0.03099668,0.0681626,0.02160865,0.001012314,0.001297127,0.0006908365,0.0002214866,0.06024478],"genre_scores_gemma":[0.9359527,0.02998248,0.01044224,0.003183935,0.001147984,0.0000311439,0.0000365074,0.0002224119,0.01900066],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4208078,"threshold_uncertainty_score":0.9998221,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03405817439892197,"score_gpt":0.3262885257455996,"score_spread":0.2922303513466777,"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."}}