{"id":"W4408518306","doi":"10.3390/sym17030450","title":"Algebraic and Spectral Analysis of a Novel Hermitian Spin Basis","year":2025,"lang":"en","type":"article","venue":"Symmetry","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"","keywords":"Basis (linear algebra); Hermitian matrix; Algebraic number; Mathematics; Algebraic analysis; Pure mathematics; Algebra over a field; Spin (aerodynamics); Physics; Mathematical analysis; 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":[0.0004478103,0.0002337308,0.0002674895,0.0007499923,0.0006621899,0.001047194,0.000524931,0.000463107,0.005586586],"category_scores_gemma":[0.00074083,0.0001362807,0.0003059195,0.0003450877,0.001458421,0.001331867,0.0008282819,0.0006113505,0.000440163],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004012413,"about_ca_system_score_gemma":0.0005192482,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000582677,"about_ca_topic_score_gemma":0.0005143302,"domain_scores_codex":[0.9997113,0.00007043735,0.00001196905,0.00004155716,0.0001125572,0.00005223542],"domain_scores_gemma":[0.9996543,0.00006081526,0.00006646328,0.00005223703,0.00009621412,0.00006999399],"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":[0.00001024461,0.00001544394,0.0001173836,0.0000147221,0.000002226294,0.00005172216,0.0000758182,0.002280634,0.002791607,0.9924706,0.0002299955,0.001939544],"study_design_scores_gemma":[0.00001823529,0.00009357089,0.0006630618,0.00002232407,0.00000524447,0.000306071,0.0002255754,0.1187995,0.002843897,0.8724471,0.004542955,0.00003232271],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.642542,0.0003968536,0.2904846,0.0009190729,0.0001645521,0.00008284992,0.0001895218,0.0001156242,0.06510487],"genre_scores_gemma":[0.9677954,0.0001916799,0.02247972,0.0001268387,0.00009466393,0.00003746222,0.00007776275,0.00003793202,0.009158411],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005586586,"threshold_uncertainty_score":0.01868904,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.026686579926906,"score_gpt":0.3404369557078649,"score_spread":0.3137503757809589,"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."}}