{"id":"W1966305649","doi":"10.1016/s0021-7824(00)00169-0","title":"Hamilton–Jacobi theory and the heat kernel on Heisenberg groups","year":2000,"lang":"fr","type":"article","venue":"Journal de Mathématiques Pures et Appliquées","topic":"Advanced Differential Geometry Research","field":"Physics and Astronomy","cited_by":204,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Heisenberg group; Geodesic; Heat kernel; Laplace operator; Mathematics; Hamiltonian (control theory); Kernel (algebra); Mathematical analysis; Pure mathematics; Mathematical optimization","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","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002602087,0.000529907,0.0006518323,0.0001515598,0.0006384639,0.0009506105,0.0005792062,0.0002023503,0.00334689],"category_scores_gemma":[0.00005515584,0.0003604898,0.0003641995,0.0002535983,0.0007982775,0.0004121343,0.0001397598,0.002002081,0.0003543008],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001505823,"about_ca_system_score_gemma":0.0001701276,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000098442,"about_ca_topic_score_gemma":0.00001456214,"domain_scores_codex":[0.9955305,0.001871211,0.0006535061,0.0004048413,0.0006089977,0.0009309756],"domain_scores_gemma":[0.9970477,0.00176602,0.0001890443,0.0004603931,0.0001140768,0.0004227453],"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":[0.002295215,0.0004599633,0.0003386633,0.0001332086,0.00045343,0.00006433446,0.005245779,0.001963353,0.0004532755,0.8819412,0.007125347,0.09952626],"study_design_scores_gemma":[0.003115376,0.0003717686,0.002828154,0.0005579236,0.000172168,0.0003710646,0.001342127,0.002076367,0.001469055,0.8532733,0.1338564,0.0005662931],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9062684,0.01523574,0.03092289,0.0156709,0.0003830732,0.001015287,0.0001146015,0.00007433039,0.0303148],"genre_scores_gemma":[0.9437566,0.0135011,0.001219332,0.001691627,0.001994294,0.000134621,0.00001806475,0.0001241674,0.03756016],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.126731,"threshold_uncertainty_score":0.9998847,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008443908298457026,"score_gpt":0.2915387977372523,"score_spread":0.2830948894387952,"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."}}