recognition_strength
plain-language theorem explainer
The ratio measuring how much the geometric mass structure exceeds the perturbative renormalization-group effect for a given fermion species. Model builders comparing phi-ladder masses to Standard Model beta functions would cite this quantity. It is obtained by dividing the geometric residue by the supplied RG parameter.
Claim. For fermion species $f$ and real number $r$, define $g(f,r) = F(f)/r$ where $F(f)$ is the geometric residue of $f$ from the mass formula.
background
The module formalizes the gap between the large geometric residue $F(Z)$ demanded by the phi-ladder mass formula and the small residue $f_{RG}$ produced by integrating Standard Model beta functions. For the electron, $F$ is near 13.95 while $f_{RG}$ is near 0.05, yielding a ratio of order $10^2$. Recognition strength is introduced precisely as this ratio, with the explicit caveat that its numerical value depends on the choice of RG endpoint and scheme.
proof idea
One-line definition that divides the geometric residue of the fermion by the supplied RG value.
why it matters
It supplies the ratio used to define electron strength and to state the structural dominance hypothesis that mass is fixed by geometry rather than perturbation. This supports the Recognition Science mass ladder on the phi scale with RG running treated as a small correction. The open question left explicit is the scheme dependence of the RG residue.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.