Time from Vacuum Entanglement: The Higgs Mass Gauge Group and Vacuum Stability from the Fisher–Bures Geometry of Sp (56,R)/U(28)

We derive the fundamental equation Δt = tP ΔS/˜η from the Page–Wootters mechanism by identifying the quantum vacuum as the universal entangled clock, with clock energy ε = EP ˜η. The parameter ˜η is an adimensional vacuum processing rate derived from quantum field theory in curved spacetime via the quantum geometric tensor (QGT) of the squeezed vacuum. The QGT on the vacuum state manifold M = Sp(56,R)/U(28) has a real part (Fisher information) that generates gravity and an imaginary part (Berry curvature) that generates gauge fields. We demonstrate four results without free parameters: (i) the Berry connection of the vacuum, pulled back from M to spacetime, undergoes dynamic holonomy reduction from U(28) to SU(3) × SU(2) × U(1) viathe Coleman–Weinberg mechanism, deriving the Standard Model gauge group; (ii) the Higgs mass ratio m2 h/m2 W = 2.370 follows from the SO(5)/SO(4) sub-system triple plus one-loop corrections weighted by gauge couplings, yielding mh = 123.8 ± 1.9 GeV; (iii) the Higgs vacuum expectation value v∗ = 248.1 GeV is predicted by marginal vacuum stability λeff (MPl) = 0 at three-loop order; and (iv) the electroweak vacuum is absolutely stable. All predictions are within 2.4% of measured values.