Vacuon Gravity: An FCC Lattice Theory of Spacetime, Gravity, Cosmology and Particle Structure

Vacuon Gravity (VG) is a quantum gravity framework that models spacetime as a face-centred cubic (FCC) elastic lattice of fundamental cells (vacuons) with spacing ℓv = 2√(ln 2) ℓP ≈ 2.691 × 10−35 m. Collective excitations of this Planck-scale medium yield several gravitational, gauge-theoretic, and cosmological observables from the discrete lattice geometry, with no free parameters and no continuum limit required. Main results in V7.1. The lattice spacing ℓv was derived from first principles in V7.0 via the Bekenstein–Hawking entropy chain and the algebraic uniqueness of the FCC cuboctahedron. The present version closes the final open derivation within the framework: the VG slow-roll parameter αCMB, defined by ns = 1 − α2CMB, is bounded analytically as αCMB ∈ [0.18670, 0.18693] from the ground-state eigenvalue of the VG Sturm–Liouville spectral problem for the l = 12 lattice mode. The Planck-observed value ns = 0.9649 ± 0.0042 corresponds to αobsCMB ≈ 0.1874, consistent with the predicted interval to within 0.59σ. The interval is obtained independently of CMB data; observations are used only for comparison. Within the current VG framework, all parameters appearing in the effective cosmological sector are fixed by the FCC lattice construction. Key falsifiable predictions (all parameter-free): ns ≈ 0.9650, r ≈ 1.58 × 10−3, and a modified tensor consistency relation r/nT ≈ −0.055 (versus −8 in standard inflation), testable by LiteBIRD and CMB-S4. Further predictions for cosmology (ηB, w0, wa), gravity (GN), and particle physics (proposed derivation of SM gauge group and generation number) are developed in the accompanying technical appendices (Parts 1–3). This core paper summarises the theoretical foundations and main results; detailed proofs and derivations are contained in the three companion volumes (Foundations, Established Results, Open Problems). V7.1 (Zenodo 10.5281/zenodo.20604060), which established ℓv at Tier A.