{"id":"W4416063083","doi":"10.1112/blms.70230","title":"Plank theorems and their applications: A survey","year":2025,"lang":"en","type":"article","venue":"Bulletin of the London Mathematical Society","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Plank; Regular polygon; Euclidean geometry; Euclidean space; Space (punctuation); Convex 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002438137,0.00128288,0.001555837,0.004968985,0.001323792,0.003256826,0.001782473,0.001745043,0.005187815],"category_scores_gemma":[0.005034195,0.000921989,0.001176713,0.006895994,0.00401513,0.006101146,0.003685455,0.003878844,0.001671306],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001893984,"about_ca_system_score_gemma":0.001301244,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00163282,"about_ca_topic_score_gemma":0.001046205,"domain_scores_codex":[0.9986367,0.0003733604,0.0001018236,0.0002990712,0.0004827615,0.0001063627],"domain_scores_gemma":[0.9970884,0.002116462,0.0001263593,0.0001578764,0.0003778687,0.0001330808],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00003264687,0.00009007,0.00144726,0.002457062,0.00007013187,0.0002264494,0.0004235673,0.003583906,0.0006223078,0.7943787,0.02370756,0.1729604],"study_design_scores_gemma":[0.00001676661,0.00006530669,0.001760675,0.001123646,0.00003198672,0.0009171758,0.0002495572,0.008110642,0.0005680828,0.7257445,0.2613557,0.00005590288],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"review","genre_gemma":"review","genre_scores_codex":[0.0108283,0.826156,0.07531825,0.006109844,0.001509545,0.00004698257,0.0002684949,0.0001449386,0.07961757],"genre_scores_gemma":[0.1303492,0.8031412,0.04140462,0.002429925,0.007262016,0.0001223569,0.0005726141,0.0002048068,0.01451321],"genre_candidate":"review","genre_consensus":"review","teacher_disagreement_score":0.005187815,"threshold_uncertainty_score":0.01735497,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008581310718105424,"score_gpt":0.2241811976648094,"score_spread":0.215599886946704,"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."}}