Edge is Everything: A Theory of Everything from One Definition

Starting from a single definition — "binary relations exist" — within ZFC set theory, we derive all 26 free parameters of the Standard Model with zero adjustable inputs. The logistic function f(x)=1/(1+e⁻ˣ), identically the Boltzmann distribution for binary variables, yields universal constants f(0)=1/2 and f'(0)=1/4. Three structural theorems and eight corrections determine all coupling constants, fermion masses, mixing angles, and the Higgs self-coupling, with a median error of 0.17% across 23 non-exact predictions. Paper I (52 pages) presents the framework, derives all parameters, and assembles the Standard Model Lagrangian. Paper II (44 pages) provides complete mathematical proofs. A Monte Carlo numerology test establishes that the probability of reproducing these agreements by chance is approximately 10⁻³³ after look-elsewhere correction.