phi_12
plain-language theorem explainer
The definition supplies φ^12 as a real scalar for pion mass ratios in Recognition Science. Researchers matching the observed m_π/m_e ratio near 273 would cite it when placing the pion on the φ-ladder. It is introduced by direct exponentiation of the self-similar fixed point imported from PhiForcing.
Claim. Let φ denote the self-similar fixed point. Then φ^{12} is the real number obtained by raising φ to the twelfth power.
background
The PionMasses module derives π⁺, π⁻, and π⁰ masses from Recognition Science via quark-antiquark binding on the φ-ladder and the GMOR relation. Pions occupy a specific rung that yields m_π/m_e ≈ 273 ≈ φ^{12}/2 after E_coh conversion. The upstream Mass abbrev simply identifies the codomain as ℝ.
proof idea
One-line definition that applies the power operator to the imported phi constant.
why it matters
This scalar supplies the numerical factor for the pion-electron ratio inside the P-013 derivation. It links the mass formula yardstick · φ^(rung-8+gap(Z)) to the observed 273 ratio and the eight-tick octave structure. No downstream theorems yet reference it.
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