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

This paper shows that the speed of light is not a primitive physical postulate but a necessary structural consequence of a closed quartic variational framework. The derivation requires no external units, no background geometry, no empirical constants, and no assumptions imported from relativity or field theory. A temporal scale arises from the lowest nontrivial spectral invariant of the Hessian, while a spatial scale is imposed by its linear symbol. Their ratio defines a universal propagation constant determined uniquely by the minimizer and by the internal invariants of the framework. The result establishes that the value and universality of the speed of light are mathematically forced rather than empirically stipulated. It follows that any theory relying on a background metric, an assumed light speed, or externally defined fundamental constants cannot be fundamental, but only derivative. The propagation constant emerges as an intrinsic invariant of the variational domain, reshaping the conceptual basis of classical and modern physics.