Abstract: We introduce the Absolute Ciaran-Genesis Conjecture (ACGC), a deterministic framework establishing primality as a stable ground-state within a 15-dimensional analytic manifold. By evolving the classical congruence models into Hyper-Modular Lattice Torsion, we define the Stability Operator ($\Xi_{AC}$) and the derived Shatter Constant ($\sigma$). Unlike probabilistic methods that rely on witness-bases, the ACGC provides a structural identity for $n \in \mathbb{Z}^+$ by measuring the "topological drift" induced by modular tetration and $E_8$ Lie algebra projections. We demonstrate that while Carmichael numbers maintain local modular symmetry, they exhibit a discrete Lattice Fracture $(\sigma_n > 0)$ when subjected to 15-stage recursive endomorphisms. This paper formalizes primality not as a factor-based property, but as a universal constant of geometric resonance.