Su(2) Saturation to Su(3) Closure: A Monte Carlo Model of Nuclear Coherence and the Emergence of Magic Numbers

We propose a minimal Monte Carlo model of nuclear coherence based on binary link interactions and triangular cyclic closure.The model exhibits a structural transition near Z = 28, where the dominance shifts from local pair coherence (link kappa) to collective triangular coherence (triangle kappa).This inversion corresponds to a spontaneous emergence of SU(3)-type hexagonal organization, without imposing any symmetry a priori.The threshold coincides with a known nuclear magic number, suggesting that shell closures may reflect geometric saturation mechanisms rather than purely combinatorial filling rules.The transition is interpreted within the TRUE framework as a crossing of the universal saturation threshold gamma zero, where local crispation yields to global relaxation through closed cyclic structures.