{"id":"W4389628202","doi":"10.1007/s00023-023-01395-x","title":"Recurrence Relations and General Solution of the Exceptional Hermite Equation","year":2023,"lang":"en","type":"article","venue":"Annales Henri Poincaré","topic":"Quantum Mechanics and Non-Hermitian Physics","field":"Physics and Astronomy","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal; Université du Québec à Trois-Rivières","funders":"Australian Research Council; Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Orthogonal polynomials; Pure mathematics; Polynomial; Hermite polynomials; Diagonal; Unitary state; Algebraic number; Algebra over a field; Recurrence relation; Mathematical analysis","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":[0.001091911,0.0006443307,0.001100183,0.001837843,0.001276748,0.002705556,0.001251361,0.00133786,0.006775072],"category_scores_gemma":[0.004764887,0.000381295,0.000675377,0.001193285,0.002081559,0.002702532,0.001405772,0.002005571,0.0008703736],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001250332,"about_ca_system_score_gemma":0.0008731509,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001586945,"about_ca_topic_score_gemma":0.001849321,"domain_scores_codex":[0.9994975,0.0001428262,0.00003809994,0.00006625472,0.0001325435,0.0001227402],"domain_scores_gemma":[0.9985756,0.0005425483,0.0003455864,0.00009757653,0.0002389188,0.0001997649],"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":[0.00003254971,0.00003068498,0.000304783,0.00003272513,0.0000123146,0.0002220956,0.0001860374,0.002073054,0.0009015201,0.9923075,0.001288063,0.002608615],"study_design_scores_gemma":[0.00002893897,0.00001567708,0.000374704,0.00001332904,0.000009268204,0.0001809957,0.00008149003,0.0246377,0.0003829451,0.9730506,0.001195303,0.0000291562],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7598819,0.003682394,0.1163199,0.005356266,0.0006448812,0.00006926606,0.0004434385,0.0004270271,0.1131749],"genre_scores_gemma":[0.9656649,0.0007556144,0.008202085,0.0003056509,0.0005505223,0.0000492658,0.0002925023,0.00009191337,0.02408767],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006775072,"threshold_uncertainty_score":0.0226649,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02924176095926519,"score_gpt":0.2666698303925749,"score_spread":0.2374280694333097,"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."}}