{"id":"W2951073213","doi":"10.48550/arxiv.math/0306431","title":"On the regularity of the polar factorization for time dependent maps","year":2003,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Fields Institute for Research in Mathematical Sciences; University of Toronto","funders":"","keywords":"Factorization; Polar; Linearization; A priori and a posteriori; Mathematics; Pure mathematics; Applied mathematics; Nonlinear system; Physics; Algorithm","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":[0.0004138262,0.0002131562,0.0002565451,0.00007703678,0.0002007827,0.0000248402,0.0008154513,0.0002421341,0.0002413549],"category_scores_gemma":[0.000336021,0.0001517622,0.0002942215,0.0002612507,0.00007000596,0.00003919281,0.0003980236,0.0003433402,0.00001953659],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001099595,"about_ca_system_score_gemma":0.00007756799,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000276206,"about_ca_topic_score_gemma":0.00001942401,"domain_scores_codex":[0.9988894,0.0002392614,0.0001834192,0.0003812908,0.000120687,0.0001859757],"domain_scores_gemma":[0.9978384,0.000514615,0.000356235,0.00109625,0.0001559909,0.00003848737],"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":[0.00003975089,0.0001450602,0.0005058189,0.0001411858,0.0001181089,0.00000231606,0.00008071509,0.003877664,0.0001319223,0.9928151,0.002134851,0.000007458978],"study_design_scores_gemma":[0.000283044,0.00004604548,0.0005552842,0.00007744945,0.0002041068,0.00000105863,0.0000746931,0.002754457,0.001547834,0.9937076,0.0005523452,0.0001960591],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8119484,0.00001628861,0.1738185,0.0002546496,0.0006205203,0.001674043,0.0003219124,0.00007753548,0.01126821],"genre_scores_gemma":[0.9883651,0.000005530501,0.0001620614,0.00005317808,0.00003026308,0.000001617105,0.00001834296,0.00001984902,0.0113441],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1764167,"threshold_uncertainty_score":0.6188684,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1150636033379572,"score_gpt":0.2017339618168157,"score_spread":0.08667035847885855,"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."}}