{"id":"W4413477184","doi":"10.1007/978-3-031-84869-8_5","title":"Algebraic Applications in Investigation of Musical Symmetry","year":2025,"lang":"en","type":"book-chapter","venue":"Springer proceedings in mathematics & statistics","topic":"Neuroscience and Music Perception","field":"Neuroscience","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Musical; Algebraic number; Symmetry (geometry); Theoretical physics; Pure mathematics; Algebra over a field; Mathematics; Computer science; Physics; Art; Geometry; Visual arts; Mathematical analysis","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003525562,0.0003350634,0.0005216144,0.0007988461,0.00006248034,0.0000597893,0.0004754386,0.0002531584,0.00004657536],"category_scores_gemma":[0.0008660571,0.0003529165,0.00005927022,0.0003335301,0.0004084426,0.0001496388,0.0002053964,0.0005978953,0.00002686458],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001566532,"about_ca_system_score_gemma":0.000159673,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006548561,"about_ca_topic_score_gemma":0.00001551702,"domain_scores_codex":[0.9975404,0.000007821857,0.0009224253,0.0006593972,0.0005699125,0.0002999997],"domain_scores_gemma":[0.9986125,0.0004131516,0.0005225578,0.0002571981,0.0001189565,0.00007563941],"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":[0.00000323617,0.00006687898,0.00009931139,0.001177096,0.000001828262,0.000006253203,0.001089595,0.000001348691,0.04093806,0.9546794,0.000385508,0.001551453],"study_design_scores_gemma":[0.0002682882,0.00005627929,0.001008189,0.001213295,0.00004853794,0.000006656265,0.0001237413,0.001345494,0.00730419,0.9849723,0.003203224,0.0004498287],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.1329569,0.0000666474,0.03201289,0.000272615,0.0008999065,0.005668447,0.0008044111,0.0003087919,0.8270094],"genre_scores_gemma":[0.5524803,0.001962967,0.2213704,0.001832421,0.0005054978,0.0008122362,0.0001096969,0.0004442713,0.2204822],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.6065272,"threshold_uncertainty_score":0.9998923,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03438343323142973,"score_gpt":0.2795229890978628,"score_spread":0.2451395558664331,"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."}}