Plottability Is Not Identifiability: Auditing the Retraining Stability of KAN Explanations

Kolmogorov–Arnold Networks (KANs) are promoted as interpretable because every edge is a plottable univariate function. We audit that claim by asking whether the plots survive retraining, and find that on tabular data the stability credited to KANs tracks additivity; we detect no contribution from the edge architecture. A plotted shape is worth reading only if retraining an equally accurate model reproduces it. We measure this retraining stability, a lower bound on disagreement over the Rashomon set, under a leakage-free protocol across 14 tabular datasets, five splits, three shape extractors (PDP, ALE, SHAP) and three bases. Spline and boosted additive models reproduce their plots; a deep KAN's do not, on 9/9 regression and 5/5 classification datasets, the gap clearing $\pm 2$ SE on 13/14 and never inverting at a common held-out loss radius. A deep KAN is no more stable than a deep MLP (7/14); an apparent $20\%$ KAN edge at high capacity coincides with the MLP carrying more parameters and is not detected near parity, against an additivity effect of $1.7$–$33.8\times$. No deep model of B-spline, RBF or Chebyshev basis approaches the spline additive reference. A matmul-only profiler misses $53$–$81\%$ of a deep KAN's operations; counting them, its arithmetic is $0.8$–$2.4\times$ the MLP's. We then draw the boundary of our own standard: the hierarchy inverts where an additive model is misspecified, the accuracy gap is often not about interactions, and controlling knot placement leaves the direction intact on 14/14 while halving a magnitude we decline to claim. The ordering holds from $6$k to $50$k rows. Finally we turn the standard on itself: four of five interaction screens reproduce their own top pairs across seeds (median Jaccard $1.00$, the fifth failing it) while agreeing with one another at $0.20$, and KAN's own prune-and-symbolify workflow—on Feynman equations, where a formula exists to find—does not converge on a structure across seeds and recovers the generating equation on at most one seed in five, while every seed's formula predicts alike. Cross-seed stability is necessary but not sufficient; a method can be perfectly reproducible and still arbitrary.