The Speed of Light as Geometric Necessity: A Derivation of c from the Crossing of Time and Gravity in the Universal Cascade, and the Unified Origin of Dark Matter and Dark Energy

The speed of light c has been measured to twelve significant figures but has never been derived from first principles. The Standard Model treats c as a free parameter — a constant of nature determined by experiment. This paper derives c from the Universal Cascade Law (Randolph, 2026a). Two cascade rates established in Paper 07 (Randolph, 2026d) govern the inter-scale coupling of physical quantities during inflation: βT = ln(δ) = 1.5410 for temporal processes and βS = δ = 4.6692 for spatial structures. Setting the rate of time emergence equal to the rate of gravitational establishment yields a unique crossing condition: τ* = 1/2. This crossing occurs at cascade level n* = nmax − logδ(2), where logδ(2) = ln(2)/ln(δ) = 0.4499 is precisely the dark matter ground-state exponent derived independently in Paper 09 (Randolph, 2026e) from 175 SPARC galaxies. c is the basin attractor of signal propagation speed in the cascade — the fixed-point velocity toward which the inflationary super-luminal expansion converged. Dark matter and dark energy are frontier cascade effects operating at the crossing scale logδ(2). The speed of light is not a constant of nature. It is a constant of mathematics: the only propagation speed consistent with the Feigenbaum geometry of time-gravity emergence.