{"id":"W2949825392","doi":"10.48550/arxiv.math/0504303","title":"A conjecture on rational approximations to rational points","year":2005,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Conjecture; Rational point; Mathematics; Point (geometry); Range (aeronautics); Variety (cybernetics); Lonely runner conjecture; Algebraic number; Pure mathematics; Collatz conjecture; Combinatorics; Mathematical analysis; Geometry; Statistics","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":[0.001812295,0.0005884658,0.0009921177,0.0009720515,0.001648541,0.002735078,0.001187862,0.001543697,0.006422696],"category_scores_gemma":[0.01454746,0.00043723,0.0008542032,0.001451189,0.006292812,0.008318193,0.003258654,0.003031005,0.0009368856],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00113324,"about_ca_system_score_gemma":0.0004100402,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00175486,"about_ca_topic_score_gemma":0.000736411,"domain_scores_codex":[0.9982443,0.0003023877,0.0001004015,0.0003948873,0.0006059731,0.0003521038],"domain_scores_gemma":[0.9959528,0.001833254,0.0003869921,0.0009740666,0.0005432282,0.0003096172],"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":[0.0001484229,0.00001916162,0.002126989,0.0001033929,0.00001574966,0.0001135378,0.0006515429,0.01166722,0.001531787,0.9700313,0.002411561,0.01117925],"study_design_scores_gemma":[0.00005361054,0.0001225368,0.001753329,0.0001088442,0.00002924843,0.0004412957,0.0006955524,0.03819423,0.003325631,0.9330135,0.02221857,0.00004356258],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5770143,0.002639127,0.2989561,0.008950587,0.0006354257,0.00006776788,0.0003915155,0.0009752579,0.11037],"genre_scores_gemma":[0.9740561,0.0009134526,0.01615672,0.0003723526,0.0002060722,0.00003644679,0.0002234355,0.00007929085,0.007956096],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006422696,"threshold_uncertainty_score":0.02148604,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03508272591058667,"score_gpt":0.2703400183440699,"score_spread":0.2352572924334832,"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."}}