Vacuum Fluctuations as the Stiffness of Spacetime: Induced Regge Gravity on the Selection–Stitch Lattice

The gravitational sector of the Selection–Stitch Model (SSM) is Regge calculus on the D4 lattice, with its action assumed. We derive it from the vacuum fluctuations of quantum fields. If the fluctuations are regulated covariantly on the piecewise-flat geometry of the lattice’s edge lengths, integrating them out induces the Einstein–Hilbert term, which, on that geometry, is exactly the Regge action. The conical heat-kernel coefficient, computed from the exact spectrum of a cone, gives the hinge action −(8πGind)−1Aδ[1+δ/4π+O(δ2)]; intersecting hinges enter only at lower powers of the cutoff. Lattice-regulated fields instead give the graviton a mass, even with their cutoff softened below the lattice scale. A defect’s verification cost, counted in proper-time ticks, couples as a rest mass and sources Einstein’s equation. The induced Newton constant is 1/Gind=CΛ2/12π. With the cutoff fixed by mode counting, the SSM’s area-law G requires C=4.2–5.9; three generations of the Spin(10) spinor with the Standard Model gauge group and a minimal Higgs give C=4, a near-cancellation that survives a mismatch of the fermion and gauge-field cutoffs between −1% and +5%. Requiring the two values of G to agree admits right-handed neutrinos and excludes supersymmetry and Higgs inflation. The covariance of the fluctuations is assumed, not derived from the lattice, and the treatment is Euclidean and one-loop.