A generative rule from affect to tactile relief: what it decides, what its spectral descriptors measure, and what classification accuracy checks

A rule that turns feeling into a surface is mathematics whose claims can be checked before anyone touches its output; such rules are often validated instead by classifying outputs. We read one rule, which maps valence and arousal affinely to the frequency, amplitude and exponent of a procedural field and exports a height map; its code being lost, we fix the field from its description. The rule has three parameters but two degrees of freedom, and a per-image min–max export removes the parameter set by valence alone. Its signed power makes the steepest slope depend on the grid unless smoothed at a chosen length. The amplitude-weighted frequency centroid measures the grid, and for non-integer frequency the domain edge, as well as the frequency. For the field without warp, the direction and order of classification accuracy were predicted beforehand with small failures; its level, computed by simulation, agreed for the classifiers it was computed for, while two qualitative level predictions failed. Accuracy checks whether an intended difference reaches a descriptor, not whether a surface conveys an emotion. We give checks for authors of such rules and propose stating the height scale, smoothing and descriptor band with the work. This is the author's original manuscript, submitted to Journal of Mathematics and the Arts (Taylor & Francis) on 27 October 2026. It has not been peer reviewed. The supplementary material is the version submitted with it. The generator, tests, results and scripts are archived separately at https://doi.org/10.5281/zenodo.23681773.