mass_ratio_geometric
plain-language theorem explainer
In the Recognition Science framework the muon-to-electron mass ratio equals phi to the eleventh power because both masses occupy fixed positions on the same phi-ladder with a rung difference of eleven. A physicist examining the origin of fermion masses would cite this result to show that the hierarchy problem reduces to geometry rather than free parameters or radiative corrections. The proof is a one-line term application of the lepton hierarchy geometric lemma.
Claim. The ratio of the muon mass to the electron mass, obtained from the mass-on-rung function on the phi-ladder, equals $phi^{11}$.
background
The phi-ladder assigns masses via the formula yardstick times phi to the power of (rung minus eight plus gap), with rung positions fixed by the ledger and phi-forcing. In this module the mass spectrum is set geometrically by the phi-ladder rather than by renormalization or Yukawa couplings. The local setting is P-013, which states that the Standard Model hierarchy problem dissolves because masses come from ledger rung positions, not from divergent loop integrals.
proof idea
The proof is a one-line term that applies the first projection of the lepton hierarchy geometric lemma from the MassHierarchy module.
why it matters
This supplies the explicit muon-electron ratio that supports the P-013 claim of hierarchy dissolution. It demonstrates that fermion mass ratios arise from the forced phi-ladder (T6 self-similar fixed point) rather than free parameters, connecting directly to the Recognition Composition Law and the eight-tick octave that fixes D equals 3. No downstream theorems yet reference it.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.