First-Principles Topological Derivation of the Speed of Light and the Laws of Thermodynamics: A Generative Digital Universe Model

We present a first-principles derivation of the vacuum speed of light c and all four laws of thermodynamics within the Generative Digital Universe Model (GDUM). Based on six axioms—the 0-dimensional Euler spiral ε₀, topological winding number W_K, projection operator Φ, projection benchmark axiom, topological evolution, and the dimensional-postulate principle—we demonstrate that c is not a fundamental constant but a unit-conversion coefficient defined by c ≡ ℓ_P/t_P. The topological critical-velocity uniqueness theorem guarantees its existence and uniqueness in 4-dimensional projected spacetime. Photons correspond to the topological ground state W_K = 1, yielding v_γ = c, while the electron velocity follows from projection efficiency η = 2πα with v_e/c = 2πα ≈ 0.0458, self-consistently linked to W_K ≈ 21.81. All thermodynamic laws emerge from topological Hilbert-space evolution: the zeroth law from winding-exchange steady states, the first law from topological functional conservation, the second law from intrinsic topological decoherence of isolated systems, and the third law from topological constraints and fluctuations prohibiting T = 0. We construct a unified topological action with no redundant statistical terms, achieving an axiomatic unification of spacetime, electromagnetism, and thermodynamics.