charged_fermion_generations
plain-language theorem explainer
The declaration establishes that three generations each containing three charged fermion species total nine particles to which the Recognition Science mass law applies. Mass spectrum modelers would cite this count when assigning rungs on the phi-ladder to the charged leptons and quarks. The proof proceeds by direct numeric normalization of the arithmetic identity in natural numbers.
Claim. Three generations each containing three charged fermion species satisfy $3 times 3 = 9$.
background
The module states Recognition Science mass predictions for Standard Model particles and compares them to PDG 2024 values. The mass law is $m(p) = $ yardstick(Sector) $times phi^{r-8+gap(Z)}$, with yardstick, rung $r$, and gap derived from three-dimensional cube geometry and charge structure. The upstream result defines Mass as the real numbers in which predictions are expressed.
proof idea
The proof is a one-line wrapper applying numeric normalization to confirm the equality in natural numbers.
why it matters
This count anchors the mass verification bundle for the nine charged fermions. It supplies the enumeration needed to apply the phi-ladder to electrons, muons, taus, and the six quarks, as documented in the module status on zero free parameters. The result aligns with the framework derivation of three spatial dimensions and the self-similar fixed point phi.
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