{"id":"W2058772407","doi":"10.1007/s12220-008-9038-7","title":"The Heat Kernel and Green Functions of Sub-Laplacians on the Quaternion Heisenberg Group","year":2008,"lang":"en","type":"article","venue":"Journal of Geometric Analysis","topic":"Algebraic and Geometric Analysis","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"","keywords":"Heisenberg group; Quaternion; Mathematics; Group (periodic table); Nilpotent; Kernel (algebra); Lie group; Heat kernel; Pure mathematics; Mathematical analysis; Physics; Quantum mechanics; Geometry","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":[0.0009844356,0.0008647846,0.001002904,0.003159794,0.001276511,0.002753266,0.001437406,0.00165285,0.004432707],"category_scores_gemma":[0.003107519,0.0003893011,0.0006658207,0.001326527,0.003558992,0.004735063,0.001595516,0.00177733,0.0006875235],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001385189,"about_ca_system_score_gemma":0.0008511839,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001588729,"about_ca_topic_score_gemma":0.0008785232,"domain_scores_codex":[0.9996145,0.0001052368,0.00001587023,0.00005470387,0.0001221986,0.00008752389],"domain_scores_gemma":[0.9985884,0.0003932239,0.0002140459,0.0001446801,0.0002554882,0.0004042069],"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":[0.00003562607,0.00002324429,0.0001916166,0.00001751826,0.000007682783,0.00006992756,0.0002656846,0.002386862,0.001123307,0.9929768,0.0004672502,0.002434412],"study_design_scores_gemma":[0.000009049464,0.00001130283,0.0002511949,0.000005202571,0.000003705268,0.00005472849,0.00008371051,0.01887614,0.0002745717,0.979908,0.0005065054,0.00001578307],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8450598,0.001500138,0.1100115,0.002566683,0.0004963594,0.00005299446,0.0001700051,0.0002195904,0.03992281],"genre_scores_gemma":[0.976912,0.0007548964,0.00565049,0.000250249,0.000568431,0.00003929304,0.00009765838,0.0001161506,0.01561081],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004432707,"threshold_uncertainty_score":0.01482886,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03281693535483197,"score_gpt":0.2552071051101166,"score_spread":0.2223901697552847,"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."}}