Quantum-Gravitational-Informational Theory (QGI): A First-Principles Framework for Fundamental Physics

We present the definitive release of the Quantum-Gravitational-Informational (QGI) framework, a fully unified and experimentally validated theory of fundamental physics based on a single dimensionless constant, αinfo = 1/(8π3 lnπ) ≈ 0.00352, derived from Jeffreys’ scale-neutral prior on the informational domain [1,π] and enforcing Ward closure ε = (2π)−3 on the phase-space measure. The resulting universal deformation ε reproduces: (i) gravitational coupling via spectral exponent δ ≈ −0.1355 from zeta-function determinants on S4, yielding Geff = G0[1 + Cgravε] with Cgrav ≈ −0.765 (informational correction weakens gravity); (ii) absolute neutrino masses mn = n2m1 with n ∈ {1,3,7} (topological winding numbers) giving Σmν = 0.060 eV and exact splitting ratio ∆m2 21/∆m2 31 = 1/30; (iii) PMNS mixing angles and CP phases from maximum-entropy principles; (iv) quark mass ratio cdown/cup = 0.590 (experimental: 0.602, error 1.97%); (v) electroweak slope δ(sin2 θW)/δ(α−1 em) = αinfo as a conditioned conjecture under BRST closure (not used to tune parameters); (vi) cosmological shifts δΩΛ ≈1.6×10−6 andheliumfraction Yp = 0.2462; (vii) gauge anomaly cancellation and prediction of exactly three light neutrino generations. A universal spectral-dimension flow ds → 4− ε was derived and tested across quantum and cosmological scales, unifying all observed effective-dimensional hierarchies as manifestations of a single informational RG-like relaxation. Our global goodness-of-fit ranges from χ2 red = 0.41 (diagonal) to 1.44 (12×12 covariance), with a Bayes factor of 8.7 × 1010 against the SM-only baseline, using 2024 PDG inputs and no continuous free parameters.