The Master Quadratic: One Equation, Two Crown Jewels — From the Diagonal of the GTE Polynomial to the Higgs Boson and Rule 110

Setting all three inputs of the GTE polynomial equal (L = C = R = x) reveals a hidden quadratic: the master quadratic m(x) = x^2 + x - 1. This single equation with discriminant 5 (the number of Standard Model fermion families) governs two crown jewels of the UGP Physics derivation tower: the golden ratio (the SRRG fixed point that seeds the electroweak scale and Higgs mass derivation) and the binary floor structure that protects Rule 110 as the unique computationally universal sub-automaton. This tutorial walks through the derivation step by step, explaining why one Z-quadratic controls both the Higgs boson mass and the universality of cellular automata computation.