PROJECT T VOLUME XIX : The Particle Lexicon Complete Algebraic Derivation of the Standard Model Spectrum from the 42 Roots of H₀(A₂)

The Standard Model of particle physics catalogues 61 elementary entities: quarks, leptons, gauge bosons, and the Higgs scalar. This inventory is phenomenological – it records what is observed, not why it exists. Volume XIX provides the algebraic derivation of every particle in this catalogue from the 42 root configurations of the affine 0-Hecke monoid H₀(A₂). We establish a complete bijection between algebraic words and physical particles, show how quantum numbers (spin, charge, color, generation) emerge as word-level invariants, and demonstrate that the 19-element discrepancy between the algebraic count (42) and the phenomenological count (61) arises from syntactic inflections: chirality mirrors and null-signifiers. The result is a Particle Lexicon – a dictionary in which every particle is a word, every interaction is a sentence, and the laws of physics are the grammar.