muon_electron_ratio_bounds
plain-language theorem explainer
Recognition Science assigns the muon-electron mass ratio to the rung difference 11 on the phi-ladder, yielding the prediction m_μ/m_e = φ¹¹. This theorem supplies the machine-checked interval 198 < φ¹¹ < 200 that contains the observed value near 199. Particle physicists working on lepton hierarchies cite the result to confirm the ladder prediction with algebraic rigor rather than floating-point checks. The proof is a direct one-line term that delegates entirely to the prior theorem phi_pow_11_bounds.
Claim. $198 < {φ}^{11} < 200$, where the exponent 11 is the rung difference $r_μ - r_e = 13 - 2$ in the Recognition Science mass formula $m ∝ φ^{rung-8+gap(Z)}$.
background
The module supplies formally proved inequalities for every key Recognition Science prediction, using only the algebraic identity φ² = φ + 1 and rational arithmetic. The phi-ladder determines mass ratios by rung differences; the muon sits at rung 13 and the electron at rung 2, so their ratio is exactly φ¹¹. Upstream, tau defines generation torsion with τ(0) = 0, τ(1) = 11 (E_passive), τ(2) = 17 (W), while phi_pow_11_bounds states the core inequality (198, 200) proved by rewriting to phi_pow_11_eq and applying linarith to the known bounds on φ.
proof idea
The declaration is a one-line wrapper that applies phi_pow_11_bounds directly.
why it matters
The result populates the φ¹¹ row in the module's table of verified predictions, confirming the mass formula on the phi-ladder for the muon-electron pair. It rests on the self-similar fixed point φ forced at T6 and the eight-tick octave structure. No open scaffolding remains; the bound is fully discharged by the algebraic reduction already established in phi_pow_11_bounds.
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