Does smoothing a convex object always reduce its number of balance points? It is an appealing intuition, but this mathematical candidate gives a precise example where the number increases.

The object is smooth, strictly convex and centrally symmetric. Its shape is specified by an explicit support function, which records the position of a supporting plane in every direction. Symmetry keeps the centre of mass fixed.

Under inward mean-curvature flow, a model in which curvature controls the speed of the surface, two new pairs of equilibria appear at opposite points. Each pair consists of a stable minimum and a saddle. The total count rises from twenty-two to twenty-six. This is a local forward-time result, not a movie of a numerical simulation. It holds for every sufficiently small positive value of the shape parameter, but the paper does not certify a numerical threshold for that phrase.

Exact symbolic calculations check the initial geometry, the relevant derivatives and the complete critical-point count. Written arguments supply the existence and continuous dependence of the flow. The endpoint counts also survive small asymmetric perturbations.

A separate probability example addresses a different question. Two random quantities can have zero means and zero covariance while the sign rule built from them has positive expected count drift. Average values alone do not determine that sign.

These distinctions matter. The original published conjecture concerns an expected count. The new work does not refute every specified stochastic abrasion model, and it says nothing about how typical these shapes are among natural rocks. Critical-point creation itself also has earlier literature.

This remains an unrefereed candidate with internal exact checks, not independent reproduction or formal verification. The paper and evidence are linked on Evidence Press. This is synthetic speech.