In the lrComparisonApp() UI, the population hair color sliders (propC1–propC5) can sum to values greater or less than 1. Since these represent probabilities, the CPT built by cpt_pop_function() assumes they sum to 1. Otherwise, resulting probabilities become inconsistent. The simple suggested fixes would be to automatically normalize with propC <- propC / sum(propC) before using it or show a validation message in the Shiny UI if the total ≠ 1. This would prevent unintended distortions and improve model accuracy.