pith. sign in
module module high

IndisputableMonolith.Foundation.AlphaDerivationExplicit

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The module derives explicit bounds showing alpha^{-1} lies in (137.030, 137.039) from the 44 pi formula forced by recognition uniqueness. Physicists deriving fundamental constants from a single functional equation would cite these results. The structure consists of a sequence of explicit definitions and lemmas that instantiate the interval using the imported Cost and Constants modules.

claim$137.030 < \alpha^{-1} < 137.039$, obtained from the $44\pi$ formula forced by the recognition uniqueness theorem.

background

Recognition Science derives constants from the J-uniqueness theorem (T5) that forces the self-similar fixed point phi and the eight-tick octave. The upstream Constants module supplies the RS time quantum $\tau_0 = 1$ tick. The Cost module supplies the J-cost and defect functions used to evaluate the 44 pi expression. The module doc-comment states that the resulting interval for alpha^{-1} follows directly from that formula.

proof idea

This is a definition module, no proofs. It assembles the interval via the sibling declarations alphaInverseLower, alphaInverseUpper, codataAlphaInverse, and alphaInverseRS that instantiate the 44 pi formula in the Cost framework.

why it matters in Recognition Science

The module supplies the explicit alpha band required by the Recognition Science forcing chain (T5 J-uniqueness to T8 D=3). It feeds the parent claim that alpha^{-1} is fixed inside (137.030, 137.039) and supports downstream use of the mass formula and Berry threshold. The doc-comment ties the result to the recognition uniqueness theorem.

scope and limits

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (8)