{"id":"W2032148870","doi":"10.1139/p01-003","title":"Exceptional algebraic properties of the three quadratic irrationalities observed in quasicrystals","year":2001,"lang":"en","type":"article","venue":"Canadian Journal of Physics","topic":"Quasicrystal Structures and Properties","field":"Materials Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Quasicrystal; Aperiodic graph; Physics; Irrational number; Algebraic number; Point (geometry); Binary number; Quadratic equation; Pure mathematics; Theoretical physics; Mathematical analysis; Condensed matter physics; Combinatorics; Arithmetic; Mathematics; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"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":[0.0002042501,0.0003284264,0.0002967567,0.0008825017,0.0008438886,0.001468195,0.0003404152,0.0003707432,0.002073186],"category_scores_gemma":[0.000786551,0.0002010839,0.0002172921,0.0004210883,0.002575113,0.0008184061,0.0007399516,0.0006527266,0.0001604194],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004313744,"about_ca_system_score_gemma":0.00019294,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003535072,"about_ca_topic_score_gemma":0.0003811527,"domain_scores_codex":[0.9996659,0.00003585029,0.00002742006,0.00006337643,0.000135233,0.00007229206],"domain_scores_gemma":[0.9995958,0.00007600505,0.0001278346,0.00007504368,0.00006823349,0.00005702797],"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":[0.0002208327,0.00005922934,0.004725944,0.0001256667,0.00001203981,0.001421882,0.001024966,0.003718212,0.08240318,0.8923319,0.0006960062,0.01326006],"study_design_scores_gemma":[0.0001214367,0.000313146,0.02416155,0.00006682717,0.00004175816,0.006466351,0.001956927,0.04626856,0.08210326,0.8240888,0.014248,0.0001633478],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9746127,0.0001001122,0.007431493,0.00008253117,0.00002165976,0.00001125286,0.00003822159,0.00006219906,0.0176399],"genre_scores_gemma":[0.9973305,0.00004074575,0.001781115,0.00001092735,0.00001453112,0.000007253854,0.00003506806,0.00001109622,0.0007687674],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002073186,"threshold_uncertainty_score":0.006935537,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05189278028321921,"score_gpt":0.2122273046277505,"score_spread":0.1603345243445313,"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."}}