{"id":"W4408444988","doi":"10.5070/c65165028","title":"Generalized polynomials and hyperplane functions in \\((\\mathbb{Z}/p^k\\mathbb{Z})^n\\)","year":2025,"lang":"en","type":"article","venue":"Combinatorial Theory","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Hyperplane; Combinatorics; Mathematics; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005806222,0.0007901953,0.0005369111,0.001470252,0.0007502811,0.00187417,0.0006908689,0.0003289513,0.006750903],"category_scores_gemma":[0.002392349,0.0002596638,0.0006613967,0.001451959,0.002313817,0.002441407,0.001567233,0.002371111,0.001011121],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00110888,"about_ca_system_score_gemma":0.0006820626,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001428323,"about_ca_topic_score_gemma":0.00145227,"domain_scores_codex":[0.9993588,0.0001209302,0.00001672735,0.0001542651,0.0001338397,0.0002155253],"domain_scores_gemma":[0.9989238,0.0003813993,0.0002295887,0.0001030753,0.0001664664,0.0001955602],"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":[0.00006399488,0.00002802156,0.0006185371,0.00005621428,0.00001013069,0.00008023923,0.0001475932,0.002558002,0.00257228,0.9763752,0.001450633,0.01603925],"study_design_scores_gemma":[0.00002823946,0.00007478533,0.002052884,0.00004137584,0.00001845546,0.0003007487,0.000168714,0.02653736,0.003218983,0.9617403,0.00577495,0.00004323099],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.676561,0.001045866,0.2599299,0.0010004,0.0003075843,0.00005768446,0.0007607355,0.0002617022,0.06007519],"genre_scores_gemma":[0.9545761,0.0008995227,0.02966962,0.0001539259,0.000360962,0.00005908134,0.0006153139,0.00007991983,0.01358552],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006750903,"threshold_uncertainty_score":0.02258402,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02421868675525911,"score_gpt":0.3070491213257261,"score_spread":0.282830434570467,"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."}}