Emergent Gravity via FCC Lattice Error Correction: Vison Excitations and the Discrete-to-Continuum Limit

We develop a gravitational sector for the SSMTheory framework, in which the FCC lattice is three-dimensional physical space and the D_4 root lattice is physical four-dimensional spacetime. The technical backbone is a single algebraic identity: the rank-four bond tensor of D_4 is exactly the unique fully-symmetric isotropic rank-four tensor. Hypercubic Z^4 fails this; even the 3D FCC sublattice fails it, with the missing pieces supplied by the twelve cross-slice neighbors. Classically, this forces the long-wavelength elastic Lagrangian to take isotropic Lamé form with equal Lamé parameters and Poisson ratio 1/5; static Kelvin strain u ~ 1/r around tetrahedral defects reproduces Newton's law. Smooth phonons are pure-gauge and cannot be the graviton. The propagating graviton is instead identified with a coherent superposition of visons—m-type excitations of the [[192,130,3]] FCC CSS code created by ceasing to measure one octahedral-void X-stabilizer. Among seven local discrete excitations of the code, the vison is the unique candidate satisfying five graviton axioms: massless, spin 2, gauge-invariant, universally coupled, and reducing to linearized Einstein-Hilbert in the continuum. A single vison produces Regge deficit arccos(-1/3) ≈ 109.47° at each of the twelve octahedral edges. The Roček-Williams theorem maps the linearized Regge action on D_4 to the linearized Einstein-Hilbert action with two transverse-traceless spin-2 polarizations and dispersion ω = c|k|. Newton's constant is fixed by Bekenstein-Hawking entropy matching to the sheet-plaquette area, giving G = a^2/(8 ln 2). The Cheeger-Müller-Schrader theorem on D_4 gives the nonlinear continuum limit; rank-four isotropy forces all O(a^2) corrections to be SO(4)-invariant, with the first cubic-anisotropic correction at O(a^4) controlled by the degree-six F_4 invariant. The one-loop graviton self-energy with first-Brillouin-zone cutoff is finite. The construction is linearized at the loop level and classical at the action level; full nonperturbative quantum gravity and the cosmological-constant hierarchy remain open.