alphaInverseUpper
The upper edge of the Recognition Science band for the inverse fine-structure constant is fixed at 137.039. Researchers tracing the alpha derivation from the J-uniqueness theorem through phi and D=3 forcing would cite this bound to close the interval check against CODATA 2022. The declaration is a direct numerical assignment with no computation or lemmas applied.
claimThe upper limit of the Recognition Science interval for the inverse fine-structure constant is $137.039$.
background
Recognition Science derives the fine-structure constant from the J-cost functional equation whose unique solution is J(x) = (x + x^{-1})/2 - 1, the forced golden-ratio fixed point phi, and the eight-tick octave that yields D = 3 spatial dimensions. The module assembles an explicit provenance chain: uniqueness theorem to phi to the 44-slot frequency structure to the closed-form alpha inverse = 44 pi exp(-8 ln(phi)/(44 pi)). The resulting band is stated as (137.030, 137.039) with the experimental value inside. Upstream definitions supply the band operation on stable states and the numerical spin value, though the present declaration is simply the constant upper endpoint.
proof idea
The declaration is a direct real-number definition that assigns 137.039 as the upper band edge; no tactics or lemmas are invoked.
why it matters in Recognition Science
The constant supplies the upper endpoint required by the AlphaProvenanceCert structure and the codata_in_band theorem to certify that the measured value lies inside the RS interval. It completes the explicit chain from J-uniqueness through phi and D=3 to the alpha formula, confirming consistency with the eight-tick octave and the predicted band width. The parent results are the structural certificate and the interval-membership theorem in the same module.
scope and limits
- Does not derive the numerical value from the 44-slot frequency formula.
- Does not prove that the CODATA value lies inside the band.
- Does not claim the bound is exact rather than an explicit upper edge.
- Does not incorporate loop corrections or higher-order terms.
formal statement (Lean)
31def alphaInverseUpper : ℝ := 137.039
proof body
Definition body.
32
33/-- The CODATA 2022 value lies inside the RS band. -/