Physical Structures Contained in the Hessian of a Harmonic Phase: a Spectral Functional Framework

This work constructs a mathematical framework based on the Hessian of the phase of a Helmholtz field in Euclidean ℝ⁴. The tensor decomposition simultaneously contains the Maxwell, Einstein, and Dirac equations as sectors of the same geometric object. From three postulates the framework derives: emergent Lorentzian metric, closed 2-form (no monopoles), Dirac equation from Helmholtz factorisation, conserved current, and falsification criteria. Quantitative predictions with zero free parameters include lepton mass ratios (2–5% deviation) and (g−2)/2 = 0.001157 (−0.20% deviation).