fermions_per_gen_eq_4
plain-language theorem explainer
The Recognition Science model assigns four Weyl fermions to each generation, matching the up, down, charged lepton, and neutrino content via the F₂² binary structure. Model builders counting total fermions against cube edges in three spatial dimensions would cite this equality to close the generation arithmetic. The proof is immediate reflexivity on the local definition of the per-generation count.
Claim. In the Recognition Science framework the number of Weyl fermions per generation satisfies $n = 4$, where this value equals $2^2$ from the binary space structure.
background
The module derives three fermion generations from the spatial dimension D = 3, identified with cube face-pairs in the RS forcing chain. A local definition sets the per-generation count to 4, interpreted as arising from F₂², while the upstream FermionKineticCert module defines the same symbol as 15 via five electroweak sectors times three colors. The module documentation states that three generations times four fermions yields twelve Weyl fermions, matching the cube-edge count.
proof idea
The proof is a one-line wrapper that applies reflexivity directly to the local definition of the per-generation count.
why it matters
This equality feeds the downstream total-fermion count and the generations-equals-D relation, completing the RS proposition that each generation contains four fermions. It aligns with the framework landmarks of D = 3 spatial dimensions and the eight-tick octave structure. No open scaffolding questions are resolved here.
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