{"id":"W4416137870","doi":"10.48550/arxiv.2506.05139","title":"Infinitesimal freeness for orthogonally invariant random matrices","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada; Agence Nationale de la Recherche","keywords":"Infinitesimal; Infinitesimal transformation; Invariant (physics); Cumulant; Term (time)","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0008435157,0.0004557947,0.0009011812,0.0002355967,0.0002552762,0.0001364052,0.000879536,0.0004485348,0.000108284],"category_scores_gemma":[0.0007357782,0.0004041571,0.0005102121,0.0003254516,0.00005847962,0.00008336326,0.0006830724,0.0005025525,0.00005465763],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005256206,"about_ca_system_score_gemma":0.0004007035,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001314227,"about_ca_topic_score_gemma":0.00009011446,"domain_scores_codex":[0.9976193,0.00009725815,0.0009066318,0.0006998109,0.0002718258,0.0004051603],"domain_scores_gemma":[0.9950329,0.002873279,0.0006255149,0.001033448,0.0003251324,0.0001097419],"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":[0.004875626,0.003421553,0.2633539,0.02766058,0.004412739,0.00006611228,0.002767253,0.002506322,0.001326054,0.5710453,0.1080753,0.01048923],"study_design_scores_gemma":[0.03046374,0.0001822692,0.03809549,0.002125293,0.004244334,0.00001911894,0.0003752111,0.006594056,0.001998411,0.7661499,0.14638,0.003372201],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8579556,0.001126463,0.1209739,0.001950917,0.0007533169,0.004780447,0.00118287,0.0004705162,0.01080603],"genre_scores_gemma":[0.8960375,0.001130756,0.07893569,0.0008922098,0.001970371,0.006725598,0.0007535439,0.0001879503,0.01336643],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2252584,"threshold_uncertainty_score":0.999841,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0919359830066892,"score_gpt":0.3497926637334826,"score_spread":0.2578566807267934,"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."}}