{"id":"W2962682765","doi":"10.4153/cmb-2007-029-6","title":"Beurling's Theorem and Characterization of Heat Kernel for Riemannian Symmetric Spaces of Noncompact Type","year":2007,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Heat kernel; Characterization (materials science); Pure mathematics; Type (biology); Kernel (algebra); Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002247773,0.0002172595,0.0007753805,0.0003833945,0.00007366769,0.000026916,0.0001804595,0.0001534837,0.001314769],"category_scores_gemma":[0.001591213,0.0001711238,0.0001758941,0.0004613289,0.000182886,0.00003271685,0.00001829212,0.000112044,0.00003523441],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004202952,"about_ca_system_score_gemma":0.0000744908,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001763484,"about_ca_topic_score_gemma":0.0002225925,"domain_scores_codex":[0.9981956,0.00006091539,0.0008469508,0.0002305437,0.0002573195,0.0004086635],"domain_scores_gemma":[0.9969421,0.00188907,0.0001887151,0.0003064118,0.0002487237,0.0004249541],"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":[0.00005412941,0.0001678279,0.0001650176,0.002195212,0.0001263691,0.000004199961,0.0007077216,4.892067e-7,0.003501829,0.9901816,0.0001457862,0.002749801],"study_design_scores_gemma":[0.0009047742,0.0003786247,0.001223299,0.0006382176,0.0004982377,0.0000273521,0.0004568331,0.003048467,0.01931463,0.9669817,0.006035285,0.0004925712],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7294633,0.00008051625,0.2558504,0.001105373,0.00005452259,0.0008076079,0.00007946949,0.00002936705,0.01252947],"genre_scores_gemma":[0.9298759,0.00001662612,0.06948583,0.00008013543,0.00005264212,0.000009414495,0.00001464626,0.00004142752,0.0004234325],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2004125,"threshold_uncertainty_score":0.9995981,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03481830116280241,"score_gpt":0.3105740383290034,"score_spread":0.275755737166201,"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."}}