Quantum Lattice Model: Routing Admittance and Saturated-Core Completion

This paper develops the geometric and dynamical completion layer of the Quantum Lattice Model (QLM) following the derivation of Lorentz kinematics from invariant lattice transport. First, a dimensionless geometric routing admittance (denoted Y) is introduced as a normalized effective admittance ratio determined purely by boundary geometry. This quantity encodes suppression of admissible phase–action transport channels without introducing new lattice primitives. Closure radii follow directly from this geometric routing structure, reproducing the reduced Compton scale under full routing and the Bohr radius under Coulomb-limited routing. Second, the universal Planck energy-density cap is promoted from a static bound to a dynamical mechanism via minimal analytic impedance blow-up. As local occupancy approaches unity, the effective impedance diverges and the geometric routing admittance collapses to zero, producing hard reflection of additional phase–action transport. Gravitational collapse therefore terminates at a finite saturated core radius scaling as M^ (1/3), set entirely by the lattice primitives h-bar, lP, and tP. The exterior solution remains exactly Schwarzschild, consistent with Birkhoff’s theorem, since the vacuum field depends only on total enclosed mass. Gravity is interpreted as asymptotic throttling of local phase–action transport, while local lattice invariants remain unchanged. No new primitives, free parameters, or modifications of exterior general relativity are introduced. This work provides the minimal geometric and dynamical closure of QLM beyond Lorentz kinematics.