recognitionStrength
plain-language theorem explainer
Recognition strength for a fermion is defined as the ratio of its geometric residue to the perturbative residue value. Physicists unifying the phi-ladder mass formula with Standard Model RG running cite this definition to quantify the non-perturbative enhancement. The definition is a direct division that implements the coupling law ratio without additional computation.
Claim. For a fermion $f$ and perturbative residue $pr$ of $f$, the recognition strength is $S(f,pr) = F(f)/pr.value$, where $F(f)$ is the geometric residue of $f$.
background
The Unification.CouplingLaw module bridges the geometric phi-ladder side of Recognition Science with perturbative SM renormalization. Geometric residue $F(Z)$ equals gap$(Z)$ from the mass formula on the phi-ladder, while perturbative residue packages a positive RG running value $f_{RG}$. The module shows that the previously unexplained ratio $F(Z)/f_{RG}$ equals the cosh enhancement $S(t)=2(cosh(t)-1)/t^2$ forced by the Recognition Composition Law and the J-cost identity $J(e^t)=cosh(t)-1$. Upstream structures supply the discrete tiers (NucleosynthesisTiers.of) and J-cost forcing (PhiForcingDerived.of).
proof idea
The definition is a one-line wrapper that divides geometricResidue $f$ by the value field of the PerturbativeResidue structure.
why it matters
This definition supplies the left-hand side for the downstream theorem coupling_law_determines_strength, which equates recognitionStrength $pr$ to coshEnhancement $pr.value$ under the hypothesis geometricResidue $f$ = coshEnhancement $pr.value$ * $pr.value$. It fills the coupling-law step in the unification chain, showing the ratio is fixed by the Taylor structure of cosh around the J-cost fixed point with no free parameters. It touches the open question of exact numerical matching between phi-ladder gaps and observed mass hierarchies.
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