Quantum Lattice Model: Geometric Routing and Gravitational Throttling in the Quantum Lattice Model

This paper develops the geometric routing and collapse-completion layer of the Quantum Lattice Model (QLM), extending the framework beyond the Lorentz kinematics previously derived from invariant lattice transport. First, a dimensionless geometric routing admittance (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 routing structure, reproducing the reduced Compton scale under full routing and the Bohr radius under Coulomb-limited routing. Second, the routing framework is extended to open radial transport. By analyzing the transverse shell geometry supporting radial propagation, an exterior routing-availability field 𝒴(r) is derived directly from lattice primitives. This routing suppression law produces the Schwarzschild critical radius and yields the gravitational constant as a derived lattice coupling expressed entirely in terms of the primitive set {ħ, ℓₚ, tₚ}. In this interpretation gravity emerges as a macroscopic manifestation of suppressed radial phase–action transport sourced by enclosed closure inventory. Third, the universal Planck energy-density cap is promoted from a static bound to a dynamical mechanism via minimal analytic impedance blow-up. As local lattice 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), determined entirely by the lattice primitives ħ, 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 therefore interpreted as asymptotic throttling of phase–action transport on the lattice, while local lattice invariants remain unchanged. No new primitives, free parameters, or modifications of exterior general relativity are introduced. This work extends the QLM framework by providing a self-consistent geometric routing, gravitational emergence, and saturation-reflection mechanism governing confinement and collapse within the reduced-action lattice structure.