{"id":"W4409126834","doi":"10.1073/pnas.2424464122","title":"Searching permutations for constructing uniformly distributed point sets","year":2025,"lang":"en","type":"article","venue":"Proceedings of the National Academy of Sciences","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"Fundação para a Ciência e a Tecnologia; European Research Council","keywords":"Solver; Point (geometry); Dimension (graph theory); Range (aeronautics); Computer science; Combinatorics; Graph; Mathematics; Inverse; Algorithm; Discrete mathematics; Applied mathematics; Theoretical computer science; Mathematical optimization; Geometry","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":[],"consensus_categories":[],"category_scores_codex":[0.001537763,0.00006962075,0.0001410351,0.0001424711,0.0002588929,0.00003685192,0.0003592676,0.00005119914,0.00001253053],"category_scores_gemma":[0.005593876,0.00004454393,0.00008222528,0.000612404,0.00034514,0.0003129649,0.00006436994,0.0001095767,3.621809e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000384066,"about_ca_system_score_gemma":0.00004775155,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001053024,"about_ca_topic_score_gemma":6.295554e-8,"domain_scores_codex":[0.9988037,0.000006271875,0.0004203635,0.0001331522,0.000526403,0.0001101631],"domain_scores_gemma":[0.9984657,0.0006589487,0.0003507434,0.000006945823,0.0004988636,0.00001879563],"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":[0.000004653307,0.00002964849,0.000120976,0.0002623479,0.00001112766,2.560254e-10,0.0002192647,0.000007654733,0.01319667,0.9850615,0.0007579338,0.0003282393],"study_design_scores_gemma":[0.0001410087,0.00001262056,0.0004360696,0.0001900886,0.00001322293,0.000001995053,0.001402679,0.01674343,0.0915869,0.8893705,0.00006145785,0.00004002392],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9010115,0.00001974093,0.009426667,0.02281776,0.00004329137,0.001368498,0.000145071,0.0000666858,0.06510075],"genre_scores_gemma":[0.9111753,0.000001100755,0.08849815,0.0001259987,0.00001238843,0.000027727,6.292717e-7,0.000002397766,0.0001563443],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09569097,"threshold_uncertainty_score":0.6696796,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09272001401368893,"score_gpt":0.3993917456826413,"score_spread":0.3066717316689523,"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."}}