A Universal Theory of Everything from the Pell-Chebyshev Wave Equation: Space, Time, Mass, Gravity, Dark Matter, and the Standard Model from p(λ) = λ2 −4λ+ 1

This manuscript presents a completely parameter-free Theory of Everything derived entirely from discrete number theory. By replacing continuous path integrals with a deterministic, topological network, the framework natively generates the fundamental observables of physics—space, time, mass, and gravity—from the structural properties of a single polynomial. It successfully unifies the Standard Model gauge symmetries, predicts a confined dark matter sector, and yields cosmological fractions that precisely match observational data. Requiring no arbitrary constants, no renormalization, and utilizing only a single physical measurement to set the universe's energy scale, this paper offers a rigorously algebraic resolution to the foundational problems of modern quantum gravity and particle physics.