{"id":"W2908439566","doi":"10.48550/arxiv.1901.00944","title":"Index Estimates for Surfaces with Constant Mean Curvature in $3$-dimensional Manifolds","year":2019,"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 British Columbia","funders":"","keywords":"Mean curvature; Mathematics; Manifold (fluid mechanics); Index (typography); Constant (computer programming); Mathematical analysis; Euclidean space; Constant-mean-curvature surface; Surface (topology); Curvature; Boundary (topology); Genus; Bounded function; Sectional curvature; Space (punctuation); Function (biology); Mean curvature flow; Pure mathematics; Geometry; Scalar curvature; Computer science","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0004632421,0.0004937292,0.000896267,0.0005626074,0.00009023522,0.00007523457,0.0005672733,0.0005872729,0.0001323345],"category_scores_gemma":[0.0001274625,0.0004286109,0.0002888779,0.0009546668,0.0001074538,0.0001507816,0.0004122732,0.0007471948,0.00002095033],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000188786,"about_ca_system_score_gemma":0.0002575965,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001664041,"about_ca_topic_score_gemma":0.0009968729,"domain_scores_codex":[0.997966,0.000070767,0.0003286896,0.0009938732,0.0001936273,0.0004470688],"domain_scores_gemma":[0.9975861,0.0007263672,0.0004420946,0.0007941488,0.0003297097,0.0001215992],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000614254,0.0005394861,0.1685786,0.001069453,0.001359707,0.0003326398,0.0003058323,0.622043,0.00002357882,0.2020318,0.003043713,0.00005806497],"study_design_scores_gemma":[0.003771979,0.0002588281,0.009566395,0.001088335,0.001695628,0.00001526491,0.001006482,0.652678,0.00008657336,0.3272831,0.0008319677,0.001717497],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9578007,0.0003422746,0.03831694,0.00007214257,0.0002466638,0.00100145,0.0001259343,0.0001042818,0.001989592],"genre_scores_gemma":[0.9938858,0.0000347217,0.003590556,0.00004503333,0.00003892368,0.000002989828,0.0001025707,0.00004899708,0.002250393],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1590122,"threshold_uncertainty_score":0.9998166,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06775963006823693,"score_gpt":0.2141400721520196,"score_spread":0.1463804420837826,"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."}}