pionElectronRatioPredicted
plain-language theorem explainer
The predicted pion-to-electron mass ratio is defined as φ^12 / 2 scaled by the ratio of coherent energy E_coh to the electron mass. Physicists working on Recognition Science hadron masses would cite this when placing the lightest mesons on the φ-ladder and checking consistency with the observed ratio near 273. The construction is a direct algebraic definition that combines the self-similar scaling forced by J-uniqueness with the fixed electron mass constant.
Claim. $ m_π / m_e = φ^{12}/2 × (E_{coh} / m_e) $, where $m_e$ is the electron rest mass and $E_{coh}$ is the coherent energy scale.
background
The Pion Masses module derives π⁺, π⁻, and π⁰ masses from Recognition Science via quark-antiquark binding on the φ-ladder and explicit chiral symmetry breaking. The module states that the pion occupies a specific rung yielding the ratio m_π/m_e ≈ 273 ≈ φ^12 / 2. The electron mass is supplied by the sibling definition electronMass_eV := 0.51099895 × 10^6 eV. Upstream imports supply the phi constant from the forcing chain and empirical program assertions that keep structures collision-free.
proof idea
This is a direct definition that evaluates the expression phi raised to the twelfth power, divided by two, then multiplied by E_coh divided by the electron mass value. No lemmas are applied beyond the imported phi from PhiForcing and the electronMass_eV constant.
why it matters
This definition supplies the explicit prediction for the pion-electron ratio in the P-013 derivation, matching the module statement m_π/m_e ≈ 273 ≈ φ^12 / 2. It anchors the φ-ladder rung for mesons inside the mass formula yardstick × phi^(rung - 8 + gap(Z)) and connects to the T6 phi fixed point and T7 eight-tick octave. No downstream theorems are yet attached.
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