gap_1332_factor
The gap-1332 resonance factor is the constant 1/(1332 phi) where phi is the golden ratio. Researchers deriving the muon g-2 anomaly resolution in Recognition Science cite this factor when assembling the RS counter-term that calibrates the phi-ladder against the observed 4.2 sigma discrepancy. The declaration is a direct one-line definition with no additional lemmas or reductions.
claimThe gap-1332 resonance factor equals $1/(1332 phi)$, where $phi$ is the golden ratio.
background
The module EA-001 treats the muon g-2 anomaly as a 4.2 sigma discrepancy resolved by phi-ladder calibration. Upstream, the gap is defined as the product of closure and Fibonacci factors that equals 45, while the anchor gap for a fermion species is the closed-form residue $F(Z) = ln(1 + Z/phi)/ln(phi)$ at the anchor scale. These supply the logarithmic mass scaling on the phi-ladder that the resonance factor multiplies.
proof idea
This is a one-line definition that directly sets the factor to the reciprocal of 1332 multiplied by phi.
why it matters in Recognition Science
The factor enters the RS counter-term definition, which supports the positivity theorem for that term and the comparison to the Standard Model reference value. It supplies the explicit numerical coefficient needed for the phi-ladder calibration step in the eight-tick octave framework that addresses the experimental anomaly.
scope and limits
- Does not derive the coefficient 1332 from first principles.
- Does not include higher-order radiative corrections.
- Does not compute the full numerical prediction for a_mu.
- Does not incorporate experimental error bars or sigma values.
formal statement (Lean)
43noncomputable def gap_1332_factor : ℝ := 1 / (1332 * phi)
proof body
Definition body.
44
45/-- **THEOREM EA-001.3**: The gap-1332 factor is positive. -/