{"id":"W2950439060","doi":"10.48550/arxiv.0708.2938","title":"Neck Pinching Dynamics Under Mean Curvature Flow","year":2007,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Curvature; Surface of revolution; Motion (physics); Flow (mathematics); Mean curvature flow; Dynamics (music); Point (geometry); Process (computing); Mechanics; Geometry; Mathematics; Classical mechanics; Physics; Mathematical analysis; Mean curvature; Surface (topology); Computer science; Acoustics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002711546,0.0003983321,0.0004203305,0.0007242151,0.000657399,0.0007969008,0.0005009457,0.0009771269,0.002357092],"category_scores_gemma":[0.001935243,0.0002723301,0.0004721973,0.0002541794,0.001374518,0.001372,0.001361716,0.0006761064,0.0002522875],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001067961,"about_ca_system_score_gemma":0.0004743426,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00230018,"about_ca_topic_score_gemma":0.0007211111,"domain_scores_codex":[0.9998285,0.00002651531,0.000005409264,0.00002978508,0.00004757159,0.00006235214],"domain_scores_gemma":[0.9996761,0.00008436591,0.00009385526,0.00003239177,0.00004881649,0.00006435357],"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":[0.0002943485,0.00004881968,0.004409337,0.0001738961,0.00003949401,0.00133022,0.001351564,0.2302731,0.0714901,0.6679215,0.002701762,0.0199659],"study_design_scores_gemma":[0.00006133463,0.0002572752,0.00548036,0.00004477847,0.00002655008,0.0009225776,0.0004421726,0.7667657,0.01364365,0.2075656,0.004705023,0.00008494592],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8401576,0.0006304565,0.1428365,0.0006158185,0.00008094421,0.00006027099,0.00009905441,0.0003248269,0.01519454],"genre_scores_gemma":[0.9915835,0.0002264101,0.004728241,0.00004542272,0.00002386818,0.00002580171,0.00004432597,0.00003665239,0.003285742],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002357092,"threshold_uncertainty_score":0.007885277,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0684180996347859,"score_gpt":0.317639614499591,"score_spread":0.2492215148648051,"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."}}