{"id":"W7117299197","doi":"10.1073/pnas.2525032122","title":"Universality for Taylor coefficients of rational functions under perturbations","year":2025,"lang":"en","type":"article","venue":"Proceedings of the National Academy of Sciences","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"Simons Foundation","keywords":"Universality (dynamical systems); Singularity; Rational function; Computation; Symbolic computation; Homogeneous; Term (time); Algebra over a field","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":[],"consensus_categories":[],"category_scores_codex":[0.0008473656,0.00007513034,0.0001685668,0.0001717946,0.0002283243,0.000009020245,0.0004989172,0.00006452346,0.000009295726],"category_scores_gemma":[0.002984659,0.00005527204,0.00009702343,0.0008859095,0.0005560717,0.0002334679,0.0000960299,0.00007855723,2.383658e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006302817,"about_ca_system_score_gemma":0.00007701891,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":7.222669e-7,"about_ca_topic_score_gemma":5.295007e-8,"domain_scores_codex":[0.9986531,0.000005822381,0.0004029711,0.0001499724,0.0006921358,0.00009601172],"domain_scores_gemma":[0.9975417,0.001019334,0.0005122731,0.00001274032,0.0008979121,0.0000160049],"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":[0.00001174316,0.0001283495,0.0001533163,0.0001545282,0.0000232392,1.541312e-10,0.00009827138,0.000328159,0.02246049,0.975551,0.001049015,0.00004186355],"study_design_scores_gemma":[0.0002747793,0.00002512097,0.001176073,0.00008189115,0.00003583342,3.757532e-7,0.0004606123,0.0030482,0.04505894,0.9496123,0.0001800098,0.00004582635],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8746162,0.00011104,0.05859434,0.01540344,0.0004930662,0.00258365,0.0003693835,0.00008824887,0.04774063],"genre_scores_gemma":[0.9811515,0.000001392331,0.01782432,0.00006386652,0.0000251269,0.00001917649,2.814039e-7,0.00000333753,0.0009110087],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1065353,"threshold_uncertainty_score":0.3573131,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08509737898809766,"score_gpt":0.3695110230208873,"score_spread":0.2844136440327896,"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."}}