muon_electron_ratio
plain-language theorem explainer
The muon-electron mass ratio is assigned the value of the golden ratio to the eleventh power. Researchers modeling lepton hierarchies or the proton radius puzzle cite this assignment. The declaration is a direct definition with no reduction steps or tactics applied.
Claim. The muon-to-electron mass ratio is defined as $m_μ / m_e = φ^{11}$, where $φ$ is the golden ratio fixed point.
background
Recognition Science assigns lepton masses to rungs on a phi-ladder whose spacing follows from the self-similar fixed point phi that satisfies the Recognition Composition Law. The electron is placed at rung 2 and the muon at rung 13, so the rung difference of 11 fixes the mass ratio. This proton-radius module imports the assignment to relate muonic atoms to the charge-radius puzzle.
proof idea
The declaration is a direct definition that sets the ratio equal to phi raised to the eleventh power. It functions as a one-line wrapper that re-exports the equality already established in the lepton mass ladder.
why it matters
The definition supplies the fixed ratio required by the lepton masses from ladder theorem that resolves the P-011 hierarchy problem, giving m_μ/m_e ≈ 199 and m_τ/m_e ≈ 3571. It also enables the muon-heavier and muonic-smaller statements that justify muonic probes of shorter distances inside the proton. The exponent 11 traces to the cube geometry of the eight-tick octave and the three spatial dimensions fixed by the T0-T8 forcing chain.
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