{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006862521,0.00008091001,0.0001574485,0.00001444903,0.0001328947,0.00005445861,0.0005512654,0.00004961245,0.00009578779],"category_scores_gemma":[0.0001424363,0.00004610142,0.0001434009,0.0003421508,0.0001045578,0.00001708891,0.0003059802,0.00007235338,0.00001708378],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000121971,"about_ca_system_score_gemma":0.00002528977,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001598107,"about_ca_topic_score_gemma":0.000001026537,"domain_scores_codex":[0.9992946,0.0001049583,0.0002158042,0.0001659945,0.000128108,0.0000904929],"domain_scores_gemma":[0.9986777,0.0007336243,0.0000903507,0.000381024,0.00009106602,0.00002621563],"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":[0.000001966419,0.00008621875,0.0003964464,0.00005412717,0.00007033992,1.15572e-8,0.000245658,0.00008681067,0.00003508391,0.9873752,0.01043638,0.001211742],"study_design_scores_gemma":[0.0005973417,0.00001550405,0.008119411,0.0000899553,0.00004472507,0.000003345224,0.0001369234,0.1905849,0.0008881161,0.7501933,0.04909965,0.0002267837],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0003648,0.0001353925,0.9814938,0.01365492,0.00002075913,0.000197538,0.000007693158,0.00003336927,0.00409173],"genre_scores_gemma":[0.6102391,0.0002624838,0.363528,0.009651667,0.0000623441,0.0002209689,0.0000179575,0.00002194727,0.01599553],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.6179658,"threshold_uncertainty_score":0.1879961,"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."}}