From the Arithmetic Substrate to Particle Masses: The GTE Cascade and the Nine Charged-Fermion Masses

The Universal Generative Principle (UGP) is a number-theoretic sieve that, starting from a single integer ridge level n, severely restricts which starting triples are internally self-consistent — and identifies our universe as the unique self-consistent solution. The Standard Model of particle physics requires approximately 25 numerical constants that cannot be derived within the Standard Model itself; the masses of the nine charged fermions (three charged leptons and six quarks) are among the most mysterious. This tutorial provides a step-by-step guide to the GTE Cascade: the sequence of derivations that connects the arithmetic substrate of the GTE polynomial through the SRRG fixed point, the Phi_MDL vacuum, and the electroweak scale to produce specific numerical predictions for all nine charged-fermion masses without free parameters.