Informational Geometry

The holographic fibration H = M 4 ×σ F, where F = (0, 1] carries the Fisher–Rao metric of information geometry, is taken as the fundamental geometric structure. Four axioms (informational content, holographic saturation, factorisation, and smoothness) fix the conformal factor σ(x) and the Hertault angle θH = arccosp2/3 as functions of d = 3 alone. The spectral theory of the Laplacian on F, the representation theory of the Hertault algebra h3 ∼ su(2) ⊕ u(1), and the ’t Hooft anomaly cancellation on S2 × F determine the Standard Model gauge group SU (3) × SU (2) × U (1) and the number of fermion generations n = 3. The Rosen–Morse potential on the fibre yields a unique bound state whose instanton tunnelling generates the electroweak VEV with the hierarchy MPl/vH ∼ e4π2. The QED vacuum polarisation running from the geometric α(0) = sin θH /(8π2) to α(MZ ) closes the gauge boson mass derivation: mW to 0.08%, mZ to 0.42%. The Weinberg dimension-5 operator with a see-saw scale Λ = αs · α3 ∗ · MPl derived from the fibration gives the absolute neutrino mass m3 = 49.88 meV (0.7%). Baryogenesis proceeds through Dark Boson–assisted electroweak symmetry breaking with ηB of order 6 × 10−10. The strong CP problem is resolved by the informational axion.