{"id":"W4379653734","doi":"10.1007/s00454-023-00509-w","title":"From the Separable Tammes Problem to Extremal Distributions of Great Circles in the Unit Sphere","year":2023,"lang":"en","type":"article","venue":"Discrete & Computational Geometry","topic":"Quasicrystal Structures and Properties","field":"Materials Science","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Unit sphere; Combinatorics; Circle packing; Mathematics; Unit (ring theory); Separable space; Disjoint sets; Spherical trigonometry; Dimension (graph theory); Hypersphere; RADIUS; Sphere packing; Great circle; Unit vector; Packing problems; Euclidean geometry; Convex body; Unit cube; Euclidean space; Geometry; Regular polygon; Mathematical analysis; Computer science; Convex hull","routes":{"ca_aff":true,"ca_fund":true,"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":[0.00103511,0.0005037764,0.0007364503,0.001280613,0.001041945,0.002317119,0.001387303,0.001449917,0.006927712],"category_scores_gemma":[0.006931453,0.0004034039,0.0003587667,0.0007806456,0.003681878,0.003929311,0.002131597,0.002058005,0.0004200557],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001126057,"about_ca_system_score_gemma":0.0006389554,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001223337,"about_ca_topic_score_gemma":0.001065585,"domain_scores_codex":[0.9995415,0.0002062321,0.00001410068,0.0000780266,0.00009354793,0.00006659689],"domain_scores_gemma":[0.9973989,0.001694778,0.0002566697,0.0001672349,0.0002065062,0.0002759242],"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":[0.00002581527,0.000007563936,0.0001134935,0.00002564429,0.000003346626,0.00002730854,0.00008601161,0.004077665,0.000154417,0.9923252,0.00105541,0.002098126],"study_design_scores_gemma":[0.000008653585,0.000005800015,0.000109803,0.000006452281,0.000001285911,0.0000295559,0.00005922236,0.02086414,0.00010573,0.9782331,0.0005716134,0.000004726445],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6722465,0.001695957,0.2459178,0.005952366,0.0002236319,0.00004523073,0.0004308357,0.0002499002,0.07323772],"genre_scores_gemma":[0.9720775,0.0006431399,0.01512992,0.0002784043,0.0003617302,0.00003688696,0.0002676367,0.0001353968,0.01106933],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006927712,"threshold_uncertainty_score":0.02317548,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02616870058225178,"score_gpt":0.2769938142402416,"score_spread":0.2508251136579898,"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."}}