IndisputableMonolith.Foundation.QRFT.FermionKineticCert
The module certifies the fermion kinetic term in QRFT by fixing the number of Weyl fermions per generation at 15 to match Standard Model counting. Researchers deriving particle content from the Recognition Science phi-ladder would cite it when linking mass formulas to fermionic degrees of freedom. The module consists of definitions for fermion counts and masses together with positivity lemmas.
claimThe number of Weyl fermions per generation is $n_f = 15$, with fermion masses given by $m_f(r) = y_0 · ϕ^{r-8+gap(Z)}$ on the phi-ladder.
background
The module imports the Cost module, which supplies the J-cost functional J(x) = (x + x^{-1})/2 - 1 for defect distances, and the Constants module, which fixes the RS time quantum τ₀ = 1 tick. It introduces sibling definitions fermionsPerGeneration, fermionMassAt, and FermionKineticCert that place fermions on the phi-ladder using the yardstick mass formula. The local theoretical setting is the QRFT extension of the forcing chain (T0-T8) that enforces D = 3 and the eight-tick octave.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the fermionic content that integrates with the RCL composition law and the T8 forcing of three spatial dimensions. It feeds the main IndisputableMonolith construction by providing the 15 Weyl fermions per generation required for kinetic certification on the phi-ladder.
scope and limits
- Does not derive the count 15 from the forcing chain axioms.
- Does not address gauge interactions or Yukawa couplings.
- Does not treat neutrino masses or generational mixing.
- Does not extend the certification beyond the kinetic term.