This paper presents a theoretical breakthrough and a paradigm upgrade based on our previous work concerning the V/E/O three-operator geometric iteration system and the discovery of geometric fixed points. The transcendental shape parameter $$p=\log_{\frac{25}{18}}4\approx4.2200$$ was algebraically derived in our prior research. Further phase-space dynamical analysis invalidates the initial hypothesis that the iteration absolutely converges to a static $$L_p$$ superellipse. Under the constraints that the initial geometry is a centrally symmetric and strictly convex polygon and that the iteration weights of the V and E operators are set equally at 1:1, we complete rigorous mathematical proofs based on discrete dynamical system theory and finite algebraic group theory.