THE DERIVATION OF SCHRÖDINGER'S EQUATION FROM SCALE-EXTENDED GEOMETRY

We present a complete derivation of the Schrödinger equation from scale-extendedgeometry. The central claim is that quantum mechanics is not fundamental — it is thelow-energy effective theory obtained by projecting scale-extended dynamics onto theobservable slice ζ=0. The wavefunction Ψ(x,ζ,t) lives in an extended Hilbert space whereζ = ln(E/E0) is the logarithmic energy scale coordinate. The scale Laplacian L_K, withweight K(ζ) = |ψ_KB(ζ)|2 given by the graviton probability density, has a compu