{"id":"W2950655538","doi":"10.48550/arxiv.1205.5474","title":"Contracting the boundary of a Riemannian 2-disc","year":2012,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Geodesic; Boundary (topology); Mathematics; SPHERES; Point (geometry); Combinatorics; Geometry; Mathematical analysis; Physics","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":[],"consensus_categories":[],"category_scores_codex":[0.0008166717,0.0002817461,0.0005748799,0.0002193423,0.0001959271,0.00005610668,0.0007591643,0.0003155341,0.0003134817],"category_scores_gemma":[0.0003666161,0.0002187332,0.0005127466,0.000735398,0.0001789877,0.0001453224,0.0006496509,0.0008319987,0.00003686651],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008649781,"about_ca_system_score_gemma":0.0001201236,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001579485,"about_ca_topic_score_gemma":0.00009575269,"domain_scores_codex":[0.9985843,0.0001763272,0.0003322935,0.0004247101,0.0001435063,0.0003388684],"domain_scores_gemma":[0.9972718,0.0006103055,0.0007443219,0.001050264,0.0002138072,0.0001095511],"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":[0.0002232553,0.001460336,0.04075309,0.00152515,0.004406198,0.0002302353,0.004999629,0.01254318,0.0001225648,0.9202488,0.01072519,0.002762338],"study_design_scores_gemma":[0.00229996,0.0001158773,0.01844498,0.0008089726,0.008877557,0.00002877092,0.009988718,0.04106598,0.0003449787,0.8827721,0.03292968,0.002322396],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9399505,0.0006662576,0.03738482,0.0001488773,0.0005019512,0.0004168305,0.0000369607,0.00008320268,0.02081063],"genre_scores_gemma":[0.9963688,0.00007431787,0.0003468025,0.00003541568,0.0001798893,7.991816e-7,0.00001257485,0.00002565417,0.002955724],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05641834,"threshold_uncertainty_score":0.8919683,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1223969809747731,"score_gpt":0.2233078806512985,"score_spread":0.1009108996765254,"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."}}