{"id":"W4396834828","doi":"10.1016/j.indag.2024.05.002","title":"The refined solution to the Capelli eigenvalue problem for <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e390\" altimg=\"si22.svg\"> <mml:mrow> <mml:mi mathvariant=\"fraktur\">gl</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>|</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">⊕</mml:mo> <mml:mi mathvariant=\"fraktur\">gl</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>|</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e422\" altimg=\"si23.svg\"> <mml:mrow> <mml:mi mathvariant=\"fraktur\">gl</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>|</mml:mo> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math>","year":2024,"lang":"lv","type":"article","venue":"Indagationes Mathematicae","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Ottawa","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Subalgebra; Lie superalgebra; Combinatorics; Eigenvalues and eigenvectors; Basis (linear algebra); Algebra over a field; Superalgebra; Pure mathematics; Affine Lie algebra; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch","metaepi_narrow","metaepi_broad","sts","scholarly_communication","open_science","research_integrity","insufficient_payload"],"consensus_categories":["metaepi_narrow","sts","open_science","research_integrity","insufficient_payload"],"category_scores_codex":[0.01543572,0.008365186,0.003490653,0.00520611,0.01296969,0.01332151,0.01600167,0.01698526,0.2127342],"category_scores_gemma":[0.01356382,0.01456647,0.01284697,0.0102794,0.01166722,0.01043258,0.01393455,0.01345513,0.0151515],"about_ca_system_candidate":true,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003350107,"about_ca_system_score_gemma":0.0103153,"about_ca_topic_candidate":true,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.008105115,"about_ca_topic_score_gemma":0.008008921,"domain_scores_codex":[0.9364288,0.004074756,0.01462966,0.01296477,0.01579463,0.01610742],"domain_scores_gemma":[0.9476275,0.01393679,0.01518774,0.0123862,0.002382787,0.008478909],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.0076193,0.00258072,0.0000336494,0.008342479,0.01037742,0.005361975,0.007500866,0.00585298,0.006928591,0.6201445,0.3187587,0.00649887],"study_design_scores_gemma":[0.01151503,0.008785213,0.0001555302,0.01056275,0.01510785,0.01639486,0.01188809,0.09207167,0.7817957,0.01513495,0.02290636,0.01368202],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6071892,0.01243928,0.01442786,0.006537969,0.0184484,0.001236376,0.008440292,0.004279713,0.3270009],"genre_scores_gemma":[0.9170795,0.008380312,0.01690962,0.007548196,0.0136541,0.01606811,0.01054981,0.008305983,0.001504364],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7748671,"threshold_uncertainty_score":0.9985,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01841206164826109,"score_gpt":0.2540611858345552,"score_spread":0.2356491241862941,"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."}}