{"id":"W3135851071","doi":"10.1017/s1446788721000215","title":"ON HIGHER DIMENSIONAL ARITHMETIC PROGRESSIONS IN MEYER SETS","year":2021,"lang":"en","type":"article","venue":"Journal of the Australian Mathematical Society","topic":"Quasicrystal Structures and Properties","field":"Materials Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"MacEwan University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Euclidean geometry; Arithmetic progression; Lambda; Set (abstract data type); Rank (graph theory); Arithmetic; Cover (algebra); Combinatorics; Discrete mathematics; Geometry; Computer science","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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0004479485,0.0001149769,0.0002467127,0.00001036393,0.0001051819,0.00007662168,0.0002665016,0.00008971547,0.002999443],"category_scores_gemma":[0.0001471865,0.00005567767,0.0003046415,0.0001428638,0.0001323323,0.00008697771,0.0001055072,0.0003433019,0.00004084568],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006541876,"about_ca_system_score_gemma":0.00007176081,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001753773,"about_ca_topic_score_gemma":8.435752e-7,"domain_scores_codex":[0.9986039,0.0001293394,0.0004152735,0.0001130832,0.0005158314,0.0002226121],"domain_scores_gemma":[0.9992819,0.0001524114,0.0001897106,0.0001932585,0.00008847178,0.00009426383],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001877708,0.001546388,0.0008352443,0.0005285213,0.0001725626,0.0003379026,0.003647155,0.002377555,0.8113865,0.04133962,0.1365561,0.001084716],"study_design_scores_gemma":[0.001737526,0.0002999399,0.02032837,0.002145753,0.0001371681,0.0009351556,0.0007049631,0.0002814416,0.2673894,0.6964688,0.009081872,0.0004895397],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9893984,0.00008125434,0.00001205806,0.009760986,0.0004105108,0.00007225898,0.000005530213,0.000006086169,0.0002529215],"genre_scores_gemma":[0.9877825,0.000003702747,0.008711575,0.0006120442,0.00008956931,0.000001990418,2.66774e-7,0.0000104822,0.002787897],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6551292,"threshold_uncertainty_score":0.9979119,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03111678332382916,"score_gpt":0.2907152224852456,"score_spread":0.2595984391614164,"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."}}