Black holes in the FCC selection–stitch model: Bekenstein–Hawking entropy, geometric evaporation, and primordial-black-hole signatures

Abstract We develop the black-hole sector of the Face-Centered Cubic (FCC) Selection–Stitch Model (SSM), a discrete-spacetime framework in which the vacuum is a close-packed lattice carrying the [[192, 130, 3]] CSS stabilizer code, treated here as a working assumption rather than an established result. Two structural results are established first. (i) We show that the four-dimensional $$D_4$$ D 4 root lattice — whose constant-time slice is the FCC lattice — supports emergent linearized gravity when treated as an intrinsic (Regge) simplicial geometry: the rank-four bond tensor is exactly isotropic, the graviton is the incompatible sector of the edge-length field, the Regge action is itself selected — it is the unique member of the local frustration-linear family that admits a flat vacuum with a covariant linearized limit — and on an explicit simplicial subdivision the continuum kinetic operator equals the linearized Einstein operator term by term, a symbolic identity with the ghost-free Fierz–Pauli coefficients. (ii) Integrating out the lattice modes generates a Sakharov-induced Newton constant proportional to the squared lattice spacing; matching it to the observed Newton constant fixes the bond length $$L_0$$ L 0 at the Planck scale up to a single O (1) coefficient, with no horizon input, and matching the bond-level Ryu–Takayanagi relation to the Bekenstein–Hawking normalization then pins that one number, $$L_0\simeq 1.843\,\ell _P$$ L 0 ≃ 1.843 ℓ P ; applying the same relation at the horizon scale gives $$S=A/(4\ell _P^2)$$ S = A / ( 4 ℓ P 2 ) with no further free parameter. The coefficient rests on that postulate and the calibration rather than on the lattice; what the lattice supplies is the compatibility of the two, its orientation-averaged bond count reducing to the RT-cell count by a computed ratio. An SSM black hole is a region in which the lattice has crossed its metric wall: Viewed from outside, it is a $$K=0$$ K = 0 topological vacancy, viewed from inside an inert $$\mathbb {Z}_2$$ Z 2 codespace, the two descriptions dual across the horizon. The same horizon supports a non-thermal evaporation channel: the intact lattice exerts a surface tension on the vacancy boundary, giving a lifetime $$\tau \propto M^2$$ τ ∝ M 2 . A faceted, curvature-driven boundary then has a classical terrace-nucleation barrier proportional to the horizon radius, producing an exponential freeze-out once the horizon exceeds a scale $$\xi \sim 1$$ ξ ∼ 1 fm; the error-correcting code may supply a quantum modification, but the corresponding dynamical conversion sequence is not derived, and we show by direct computation that static code quantities do not grow with horizon size. Phenomenologically this is a two-parameter evaporation law — an unsuppressed $$\tau \propto M^2$$ τ ∝ M 2 channel below $$\xi $$ ξ and an exponential freeze-out above it — with two testable consequences. For the hypothesis $$\xi \sim 1$$ ξ ∼ 1