Quantum Lattice Model: Geometric Routing Admittance and Hard-Core Reflection

This paper develops the geometric routing and reflection layer of the Quantum Lattice Model (QLM), extending the framework beyond Lorentz kinematics derived from invariant lattice transport. First, a dimensionless geometric routing admittance (denoted YYY) 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 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 M1/3M^1/3M1/3, determined entirely by the lattice primitives ℏℏ, ℓPPℓP, and tPtPtP. 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 extends the QLM framework by providing a self-consistent routing and reflection mechanism governing confinement and collapse within the reduced-action lattice structure.