Twenty Words: Derivation of the Alphabet Code of Particles and Antiparticles

This study derives, from the four-letter alphabet {2, 3, π, ln 2} of the ΨD (Dimensional Flow Cosmology) framework, the complete count of the fundamental particle catalog, its order of formation, its threegeneration structure, and its electric charges; it lays out the gate profiles with an accounting that separates, cell by cell, the derived and the assigned items. The document is a counting and accounting document: no dynamical law, coupling strength, or scale is produced; “derivation” is confined to combinatorial structure and intra-rule necessities. The founding propositions: the alphabet grows by a ladder (d+1 letters at level d); a word is three unordered digits; the catalog closes under selection with repetition as 1 → 4 → 10 → 20. Seventeen products coincide, in a species-level count, with the number of fundamental fields of the Standard Model; the nine-cell block of massive fermions is filled completely by three types and three modes; the number of generations follows from the number of modes. The electric charges fall out as the unique solution of three structural inputs: {+2/3, −1/3, −1, 0}; two inputs are imported — the unit step of the W and the observed value of the color multiplicity — and the established counterpart of mode closure is anomaly cancellation. The halt law admits no exception: a word that carries the boundary letter but no measure letter is written to the halt class; the pure axis triple is the lattice. Antiparticles open no address in the catalog: the antiparticle is the mirror-direction reading of the word — mass equality falls from the definition, sign reversal from the reading; pair production is joint writing in two opposite directions. The spin reading is derived by two independent routes, the neutrino spectrum is canonized by a single pre-registration (Σm ≈ 0.0596 eV), and the mass ratios are reduced to leading order. The closure of the catalog at twenty is an open prediction: there is no new fundamental particle; the framework’s sharp, distinctive content is the ν₁ ≈ 0.79 meV end of the spectrum tied to the edge condition, whose derivation remains an open item. The ledger language is bound to physical counterparts through a lexicon, the wording of the rules is frozen, and the structural rulings are verified by script.