Geometric Emergence of Spacetime Scales: Speed of Light Renormalization, the Planck Scale, and the Two-Step Mass Limit of Quantum Decoherence

For decades, theoretical physics has struggled to discretize spacetime without

inadvertently breaking Lorentz invariance [1,2]. Building upon the Selection-Stitch

Model (SSM) [3], we model the vacuum as an emergent Face-Centered Cubic (FCC,

K = 12) tensor network. In this unified framework, we demonstrate that the foun-

dational scales of both relativity and quantum mechanics emerge naturally from the

strict geometric limits of this saturated lattice. First, we show that the macroscopic

speed of light (c) is simply a geometric renormalization of the underlying lattice

hopping speed (c = 4vlattice). Second, rather than treating the Planck scale as an

arbitrary mathematical cutoff, we derive the fundamental lattice spacing L≈1.84lP

from the exact Ryu-Takayanagi holographic entanglement map [6]. Third, by treat-

ing the vacuum as a Chiral Cosserat continuum, we explicitly derive the complex

unit i and the Schr¨odinger equation from lattice gyroscopics. Finally, by intersect-

ing this wave mechanics with the lattice’s absolute L/√3 kinematic exclusion limit

(the metric wall) [4], we predict a strictly falsifiable, two-step decoherence limit

for macroscopic superposition: the onset of dimension-8 structural corrections at

msoft ≈11.8µg, and an absolute structural hard cutoff at mhard = √3msoft ≈20.5µg.