pionMassPredicted_eV
plain-language theorem explainer
The definition supplies the predicted pion mass in eV as the coherence energy scaled by phi to the twelfth power and halved. Physicists deriving hadron masses on the Recognition Science phi-ladder would cite this expression for the pion rung. It is a direct definition that applies the phi-ladder scaling rule without invoking additional lemmas.
Claim. The predicted pion mass in electronvolts is given by $m_π = E_{coh} φ^{12}/2$, where $E_{coh}$ is the coherence energy and $φ$ is the golden-ratio fixed point.
background
The Pion Masses Derivation module treats pions as quark-antiquark bound states whose masses follow phi-ladder patterns. The ladder assigns masses by scaling a base energy (here the coherence energy) by successive powers of phi, with the pion placed at exponent 12 relative to the electron scale. This rests on the forcing chain in which phi emerges as the self-similar fixed point and the eight-tick octave structure fixes the rung spacing.
proof idea
This is a direct definition that instantiates the phi-ladder mass formula at exponent 12 using the coherence energy as reference scale.
why it matters
The definition supplies the explicit RS prediction for the pion mass and the ratio m_π/m_e ≈ φ^{12}/2. It fills the P-013 slot in the mass-ladder construction and connects to the broader claim that hadron masses arise from phi-scaling of the coherence energy. It leaves open the precise size of electromagnetic corrections that split charged and neutral pion masses.
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