{"id":"W1592608789","doi":"10.46298/dmtcs.450","title":"Diophantine Approximation, Ostrowski Numeration and the Double-Base Number System","year":2009,"lang":"en","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Numerical Methods and Algorithms","field":"Computer Science","cited_by":13,"is_retracted":false,"has_abstract":true,"ca_institutions":"Pacific Institute for the Mathematical Sciences","funders":"","keywords":"Mathematics; Diophantine equation; Correctness; Partition (number theory); Base (topology); Integer (computer science); Combinatorics; Order (exchange); Discrete mathematics; Algorithm; Mathematical analysis; 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":"codex-gemma-dda1882f352a","candidate_categories":["scholarly_communication"],"consensus_categories":[],"category_scores_codex":[0.003122692,0.0002649902,0.0003933132,0.00007692431,0.0007061452,0.001325133,0.001622502,0.00005200754,0.00001074044],"category_scores_gemma":[0.000113313,0.0001514149,0.00009869023,0.001006368,0.002033225,0.0007064358,0.000493268,0.0002090192,0.00003878947],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003251457,"about_ca_system_score_gemma":0.00005000582,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000211985,"about_ca_topic_score_gemma":4.751289e-8,"domain_scores_codex":[0.9972706,0.0001845341,0.0005268502,0.0006545935,0.0008580327,0.0005054103],"domain_scores_gemma":[0.9979721,0.0004448797,0.0001906071,0.0009288319,0.0002168581,0.0002466628],"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":[0.00001419863,0.00004392084,0.000003027741,0.00002691285,0.000004547232,0.000004240983,0.0007878242,0.00002424582,0.000205161,0.9814942,0.000009049923,0.0173826],"study_design_scores_gemma":[0.0007361939,0.00005904338,0.00004308345,0.00005659194,0.00001115274,0.00009064047,0.00003902256,0.6791541,0.00128611,0.3183485,0.00001108024,0.0001645029],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.003817642,0.00002937472,0.9864708,0.0040201,0.0002873538,0.0004610957,0.000001270453,0.0002148759,0.004697478],"genre_scores_gemma":[0.500637,0.000002403171,0.4989848,0.0002664647,0.00008493597,0.00001169399,5.814854e-7,0.000005166358,0.000006904844],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.6791298,"threshold_uncertainty_score":0.9997116,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0113201498828838,"score_gpt":0.2691241931922988,"score_spread":0.257804043309415,"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."}}