mesonBinaryGauge
plain-language theorem explainer
The declaration sets the binary gauge factor for the meson sector to the natural number 1. Researchers deriving pion masses via the Recognition Science φ-ladder would reference this constant when scaling energies by division by 2. The definition is a direct constant assignment with no further computation or hypotheses.
Claim. The binary gauge factor for the meson sector is the natural number $1$, which implements division by $2^1 = 2$ in the φ-ladder mass formula.
background
The PionMasses module derives π⁺, π⁻, and π⁰ masses from Recognition Science by placing pions on the φ-ladder after accounting for quark-antiquark binding and explicit chiral symmetry breaking. The module states that the mass ratio satisfies m_π/m_e ≈ φ^12 / 2 and lists concrete predictions π⁺ ≈ 139.6 MeV, π⁰ ≈ 135.0 MeV. This gauge factor enters the scaling step that converts the coherent energy E_coh into the observed pion mass.
proof idea
The definition is a direct constant assignment of the value 1. It serves as a one-line wrapper that supplies the binary division exponent for all subsequent meson mass expressions in the module.
why it matters
This definition supplies the division factor required by the module's mass formula E_coh × φ^12 / 2, which reproduces the observed pion-to-electron ratio. It therefore closes one step in the φ-ladder construction that begins from the upstream theorem establishing four structural conditions from seven axioms. The choice of exponent 1 is consistent with the eight-tick octave structure of the Recognition framework.
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