{"id":"W4406829957","doi":"10.1002/eng2.13107","title":"Composition, Non‐Commutativity, and Vector Decompositions of Finite Rotations","year":2025,"lang":"en","type":"article","venue":"Engineering Reports","topic":"Mathematics and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Sherbrooke","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Commutative property; Composition (language); Vector (molecular biology); Mathematics; Pure mathematics; Algebra over a field; Biology; Genetics; Linguistics; Philosophy","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":[0.00168154,0.000419404,0.0005650783,0.001030504,0.0007395063,0.001528524,0.0006048967,0.0004204103,0.005090609],"category_scores_gemma":[0.002895744,0.0004029774,0.0008621624,0.0006299551,0.003646228,0.002335693,0.001556156,0.001042055,0.000602826],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004567667,"about_ca_system_score_gemma":0.000384937,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000746905,"about_ca_topic_score_gemma":0.000623881,"domain_scores_codex":[0.998122,0.000631643,0.0001735584,0.0003835985,0.000484476,0.0002045429],"domain_scores_gemma":[0.9987645,0.0004918948,0.0002438099,0.0001749829,0.0002458123,0.00007890996],"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":[0.00002631391,0.00001460987,0.0001228012,0.00003389927,0.000007512189,0.0000765156,0.0002435464,0.001826302,0.002114334,0.981346,0.0002926677,0.01389556],"study_design_scores_gemma":[0.00001388367,0.00005980743,0.0002250536,0.00002622607,0.0000102694,0.0001457869,0.0001476489,0.01950908,0.00383396,0.9683832,0.007626808,0.00001820357],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1208897,0.001015664,0.8483776,0.0002873423,0.000314342,0.00005884525,0.00007310444,0.0001937338,0.02878967],"genre_scores_gemma":[0.7721349,0.000995943,0.2116841,0.0002303889,0.0002717946,0.0001592565,0.000198845,0.0002030203,0.01412174],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005090609,"threshold_uncertainty_score":0.01702976,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01102739601955024,"score_gpt":0.2920119686533837,"score_spread":0.2809845726338335,"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."}}