{"id":"W4386554969","doi":"10.48550/arxiv.2309.03428","title":"Extrinsic geometry of calibrated submanifolds","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Immersion (mathematics); Nabla symbol; Mathematics; Infinitesimal; Tangent; Pure mathematics; Geometry; Riemannian manifold; Mathematical analysis; Physics; Quantum mechanics","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":[0.0003667767,0.0005019555,0.0003298743,0.001377497,0.0009501482,0.001376152,0.0004878169,0.0005404158,0.002663945],"category_scores_gemma":[0.0009446636,0.0003031479,0.0004139032,0.000412783,0.002262011,0.001471026,0.002089147,0.0009218016,0.0002864362],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001077596,"about_ca_system_score_gemma":0.0003698575,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001036257,"about_ca_topic_score_gemma":0.0007372354,"domain_scores_codex":[0.9994338,0.00007874086,0.00002965425,0.0001769432,0.0001963756,0.00008441861],"domain_scores_gemma":[0.9994097,0.00005502424,0.0001878411,0.00008902166,0.0001015146,0.0001568889],"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":[0.00002721346,0.00001444535,0.001670884,0.00001709004,0.00001307932,0.0003446886,0.0003774964,0.004934532,0.00945701,0.9788772,0.0003461913,0.003920057],"study_design_scores_gemma":[0.00003191951,0.000190412,0.01175438,0.00002416845,0.00002611558,0.001142828,0.0007231555,0.05152038,0.01186728,0.9107763,0.01187217,0.00007090602],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9433103,0.00009044591,0.03653057,0.0002270798,0.00003185824,0.00002693535,0.0001120443,0.0001164655,0.01955439],"genre_scores_gemma":[0.9903527,0.00007813813,0.004744041,0.00005733087,0.00004253502,0.00001985649,0.0001632828,0.00003831711,0.004503867],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002663945,"threshold_uncertainty_score":0.008911788,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1944658046538162,"score_gpt":0.2245895843674856,"score_spread":0.03012377971366945,"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."}}