Butterfly Filtering and Universality: A Renormalization-Invariant Functional for the Speed of Light

This companion note develops a constructive route toward a quantitative characterization of the speed of light using universality at the edge of chaos. Realization dynamics is modeled by unimodal iterative maps, and the accumulation point of the period-doubling cascade is identified as a regime where microscopic sensitivity (“butterfly effect”) is filtered by renormalization dynamics. At the critical parameter value, the realization process admits a physical invariant measure. A dimensionless functional is defined with respect to this invariant density. We show that is universal within the unimodal class and therefore independent of microscopic realization rules. The speed of light is then expressed structurally as where and belong to a calibration layer fixing physical units, while is a renormalization-group invariant. The result provides a concrete bridge between chaos, renormalization, and the emergence of universal physical constants, and complements earlier work on the metaformal origin of fundamental constants by supplying a computable, dimensionless invariant suitable for numerical determination.