Resolution of the Kepler Conjecture on Compact Sphere Packings by the Geometric Invariant Gamma Zero

This preprint presents the resolution of the Kepler conjecture within the TRUE framework. The compact packing of equal spheres in three dimensions reaches its maximum density when the K-crispation field relaxes at the universal gamma zero threshold. The analytical calculation, without recourse to exhaustive combinatorics or supercomputers, directly yields the historical value Pi divided by the square root of 18, approximately 0. 74048. The proof is obtained in three simple steps. First, the dynamic crispation operator sets the absolute elastic limit at gamma zero, namely 0. 136605. Second, the three-dimensional topological coupling factor f = 3 / π² (approximately 0. 303963) expresses the spatial constraint. Third, the critical saturation density is calculated by dₘax = 1 - (gamma zero multiplied by f). A Beurling-Selberg projection onto the discrete centers of the spheres restores the exact Kepler constant. No numerical simulation, no heavy assumptions. The gamma zero invariant solves in a few lines a conjecture that remained open for four centuries. The manuscript is deposited under CC BY 4. 0 license.