IndisputableMonolith.Foundation.QRFT.YukawaCouplingFromJCost
This module defines the Yukawa coupling for fermions at phi-ladder rungs by direct reference to the J-cost function. Researchers constructing fermion mass hierarchies and interaction strengths in Recognition Science cite these constructions when linking couplings to the underlying cost structure. The module supplies evaluation functions, upper bounds, a rung-8 specialization, and a certification type that together fix the coupling values and establish their decrease at higher rungs.
claimThe Yukawa coupling $y(r)$ for a fermion at phi-ladder rung $r$ (relative to rung 8) is obtained from the J-cost function evaluated at the corresponding scale factor.
background
The module resides in the Foundation.QRFT layer and imports the base constants together with the cost definitions. In Recognition Science the phi-ladder enumerates the discrete self-similar scales generated by successive powers of the golden ratio phi, with rung 8 fixed as the reference scale for the lightest fermions. The J-cost function quantifies recognition cost via $J(x) = (x + x^{-1})/2 - 1$ and supplies the monotonic measure from which the Yukawa coupling is extracted. The Constants module supplies the RS time quantum tau_0 = 1 tick used in all scale assignments.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The definitions supplied here feed into the fermion mass and coupling calculations that appear in the QRFT sector. They realize the link between the J-uniqueness property in the forcing chain and the observed Yukawa hierarchy by assigning lower couplings to higher rungs on the phi-ladder, thereby closing one step in the derivation of particle masses from the single functional equation of the framework.
scope and limits
- Does not compute explicit numerical values for any Yukawa coupling.
- Does not derive the coupling form from a dynamical Lagrangian beyond the J-cost.
- Does not address renormalization-group running or scale dependence.
- Does not treat boson couplings or higher-order corrections.