PROJECT T FOUNDATIONS Volume I : L'OBJET H₀(Ã₂) : The 0-Hecke Monoid of the Affine Weyl Group

This document establishes the foundational object of Project T: the 0-Hecke monoid of the affine Weyl group of type A₂, denoted H₀(Ã₂). This is the first volume in the Foundations series, which aims to place the entire theoretical framework on rigorous, formally verified ground. The central thesis of Project T is that the algebraic structure of H₀(Ã₂) encodes fundamental physics with zero free parameters. Every constant, every symmetry, every selection rule emerges from the algebra itself. Nothing is added; nothing is fitted.