{"id":"W4416038282","doi":"","title":"ALGEBRAIC INTERPRETATION OF THE TWO-VARIABLE JACOBI POLYNOMIALS ON THE TRIANGLE: THE PENTAGONAL WAY","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Interpretation (philosophy); Rank (graph theory); Algebra over a field; Subalgebra; Jacobi polynomials; Algebraic number; Representation (politics); Basis (linear algebra)","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":[0.0003165654,0.0003561293,0.0002967658,0.0008314094,0.001013176,0.001890278,0.0006758725,0.0004545137,0.007744551],"category_scores_gemma":[0.0004932936,0.0001673836,0.0004870512,0.0007809552,0.002294701,0.001739767,0.0009978537,0.001372039,0.001219601],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007784754,"about_ca_system_score_gemma":0.0006411319,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001325048,"about_ca_topic_score_gemma":0.001167868,"domain_scores_codex":[0.9997218,0.00007306576,0.000009097618,0.00003893575,0.00008703924,0.00007011965],"domain_scores_gemma":[0.9998016,0.00003138385,0.00002675545,0.00004328482,0.00005760023,0.00003956726],"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":[0.00001371246,0.000006780879,0.00004116247,0.00001169882,0.000001216057,0.00005727763,0.0001496597,0.0006589674,0.001170236,0.9946326,0.0006096971,0.002647038],"study_design_scores_gemma":[0.000006451251,0.00002358417,0.0001707419,0.00001462889,0.000002977581,0.0001988095,0.0002601291,0.01008188,0.001733317,0.9747619,0.01273168,0.00001388366],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2480959,0.001364911,0.3627586,0.003015228,0.001101888,0.00006736965,0.000334773,0.000474712,0.3827868],"genre_scores_gemma":[0.9227182,0.0006379676,0.04276258,0.0005615063,0.0003190618,0.00003468015,0.000136637,0.0001581783,0.03267115],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007744551,"threshold_uncertainty_score":0.02590811,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07088185983596886,"score_gpt":0.3232710649145585,"score_spread":0.2523892050785896,"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."}}