PERMANENT GRAVITY: A BOSONIC THEORY OF SPACETIME FROM THE CONFORMAL INVARIANT R = perm(g)/ det(g)

We develop a geometric framework based on the permanent, the symmetric analog of the determinant. The ratio R = perm(g)/ det(g) is a conformal invariant that captures the off-diagonal structure of the metric. In 2D, the action S = R√g R d2x yields non-trivial dynamics, violating the weak energy condition and naturally supporting traversable wormholes. In 4D, we construct a spectral action combining the determinant(fermions) and the permanent (bosons). The asymptotic expansion yields the Einstein-Hilbert term from the determinant, and from the permanent we obtain: (i) a conformally invariant scalar mode R, (ii) gauge fields F 2µν from off-diagonal metric components, and (iii) the Higgs potential V (ϕ) = λ(ϕ†ϕ − v2)2 from diagonal components. The resulting theory unifies gravity, gauge interactions, and electroweak symmetry breaking in a purely geometric framework, without introducing extra dimensions or supersymmetry.