r_muon
plain-language theorem explainer
The theorem fixes the muon at rung 13 on the φ-ladder used for lepton masses. Workers deriving the fermion hierarchy from Recognition Science would cite this rung to obtain the ratio m_μ/m_e = φ^11. The proof is a direct term extraction of the middle conjunct from the conjunction that verifies all three lepton rungs.
Claim. The rung integer for the muon is 13, written $r_μ = 13$.
background
The module derives fermion masses from positions on the φ-ladder, with mass proportional to φ raised to the rung integer n. The rung assignment for charged leptons places the electron at baseline rung 2, the muon at 2 + 11 = 13, and the tau at 2 + 17 = 19; the increments 11 and 17 arise from cube geometry in the forcing chain. This declaration isolates the muon value from the upstream verification that simultaneously confirms the three rung numbers by simplification over the definitions of tau and the passive-field edge counts.
proof idea
The proof is a one-line term that projects the second conjunct of the conjunction proved in the upstream r_lepton_values theorem.
why it matters
The assignment feeds the geometric hierarchy theorem, which establishes m_μ/m_e = φ^11 and m_τ/m_μ = φ^6 and thereby resolves P-002 without free Yukawa parameters. It rests on the self-similar fixed point phi and the eight-tick octave structure from the unified forcing chain.
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