The Speed of Light as an Unavoidable Spectral Ratio of the Universal Quartic Functional

We show that the speed of light is not a postulate but an unavoidable spectral ratio emerging from a closed quartic variational structure. No external scales, units, metrics, or physical assumptions enter the derivation. A temporal scale is fixed by the lowest nontrivial spectral invariant, while a spatial scale is imposed by the linear symbol generated by the Hessian. Their ratio produces a universal propagation constant,\[c_{\mathrm{em}} = \frac{L_{\mathrm{em}}}{T_{\mathrm{em}}},\]entirely determined by the minimizer and the internal invariants of the framework. No tuning, interpretation, or background geometry is permitted: the propagation constant is a mathematically forced output of the quartic functional. The result eliminates the need for any external definition of the speed of light and reframes it as a structural consequence of a self-contained variational principle.