Gravity as Emergent Topology in a Planck-Scale FCC Lattice (v8)

We derive Newtonian gravity as an emergent phenomenon of a Planck-scale face-centred cubic (FCC) lattice substrate within the Field of Resonance (FoR) framework. A massive body acts as an Eshelby elastic inclusion, producing an exterior scalar potential Ψ ∝ 1/r satisfying Laplace's equation. A test wave packet couples to this potential through a non-derivative energy interaction uniquely selected by the Speed-Invariance Theorem, yielding the Newtonian force law F = −GMm/r². Newton's constant G = c³ℓ_Pl²/ħ is derived from FCC lattice parameters without G as input. The weak equivalence principle follows as a structural consequence of the wave-packet coupling theorem. The anharmonic coupling constant α = 9/2 is derived from the collective wave-packet mechanism with full FCC elastic tensor contraction, resolving Open Problem 1. A partial resolution of Open Problem 2 is provided via the holographic principle: saturating the Bekenstein-Hawking bound at the Planck scale constrains the substrate field's interaction range to k_peak = (9π²)^(1/3)/ℓ_Pl, in agreement with the FoR geometric requirement to 0.43%. Version 8 incorporates three revisions in response to peer review. First, Section 5.4 establishes the validity regime of the continuum approximation: the FCC elastic anisotropy ratio A = 2C₄₄/C₁₁ = 1 exactly for central forces, so angular corrections to spherical symmetry vanish identically to leading order, and the Eshelby results are applied only in the far-field regime r ≥ 3r₀ ≈ 16ℓ_Pl where corrections are below 0.1%. Second, Section 7.5 clarifies the derivation of G as a structural consistency result rather than a non-circular first-principles derivation: given that the lattice spacing equals the Planck length, G emerges from the elastic mechanics without appearing as a free Lagrangian parameter, but the identification ℓ_lattice = ℓ_Pl imports G through the definition of the Planck length. Third, the holographic argument is corrected: the FCC Wigner-Seitz cell is the rhombic dodecahedron (surface area A_RD = 3√2 ℓ_Pl²), not the truncated octahedron (which is the BCC Wigner-Seitz cell), and the 0.43% figure is clarified as a parameter-constraint precision, not a per-site mode count.