Derivation of Newton's Gravitational Constant in MUT V3: Two Independent Geometric Pathways

We present the complete derivation of Newton’s gravitational constant G within the Malallah Unified Mesh Theory (MUT V3). The theory posits that spacetime is a tetrahedral lattice of entangled Bell states, with six hierarchical levels n = 0,..., 5. Using only the geometric integers Nmax = 4,

Nvac = 2, Nmin = 1 and the transcendental number π, we obtain two independent derivations of G:

(1) a bridge equation from the discrete action, and (2) a mechanistic Oobleck thread traction model. Both yield the same numerical value G = 6.67458450 × 10−11 N·m2/kg2, matching the CODATA

2018 value to 0.0043%. The derivation eliminates all free parameters and shows that the weakness

of gravity is a direct consequence of the tetrahedral geometry.