Quantum Lattice Model: Geometric Routing and Gravitational Throttling

This paper develops the exterior gravitational routing sector of the Quantum Lattice Model (QLM) by deriving gravitational throttling from geometric suppression of radial phase-action transport. Starting from the QLM primitive set {ℏ, ℓP, tP}, with c = ℓP/tP and mP = ℏ tP/ℓP², the analysis introduces a dimensionless scalar routing availability Y, defined as the fraction of vacuum routing capacity available to phase-action transport. For a spherically symmetric mass M, the mass-energy content defines a dimensionless closure inventory NM = M/mP. Radial phase-action transport is supported by transverse spherical shells of area 4πr². Because each shell has two independent transverse routing directions, the local radial routing decrement takes the form dY = -2 NM (ℓP/r²) dr. With the boundary condition Y(∞) = 1, this integrates to the exterior routing field Y(r) = 1 - 2(M/mP)(ℓP/r). The zero of this routing availability defines the Schwarzschild critical radius rs = 2(M/mP)ℓP, which is equivalent to the standard form rs = 2GM/c² when G = ℓP⁵/(tP³ℏ). Thus the Newtonian gravitational constant appears as a derived lattice coupling rather than as an independent primitive. The gravitational redshift factor is then interpreted as a routing throttle, Zg(r) = Y(r)^(-1/2) = (1 - rs/r)^(-1/2), so that local phase-action evolution remains proper-time invariant while outward transport relative to infinity is asymptotically suppressed. The finite interior endpoint of collapse is not rederived in this paper. It is supplied by the separate density-cap construction developed in Quantum Lattice Model: Planck Energy Density Cap and Minimal Saturated-Core Completion, which provides the local bound u(r) ≤ uP and the corresponding saturated-core radius. The present work therefore focuses specifically on the exterior Schwarzschild-compatible routing derivation. No new primitives, free parameters, or modifications of the exterior Schwarzschild form are introduced. Within QLM, gravity is interpreted as asymptotic throttling of radial phase-action transport produced by geometric suppression of exterior routing availability.