alpha_fifth_small
plain-language theorem explainer
The Recognition Science numerical approximation to the fine-structure constant raised to the fifth power is less than 10^{-8}. Researchers deriving QED corrections or bounding vacuum-induced energy shifts in hydrogen would cite this bound to quantify why the Lamb shift remains tiny. The proof is a one-line term-mode reduction that unfolds the approximation definition and evaluates the numerical inequality directly.
Claim. Let $a$ denote the Recognition Science numerical approximation to the fine-structure constant. Then $a^5 < 10^{-8}$.
background
The module derives the Lamb shift from vacuum J-cost fluctuations of the ledger, where electron jiggle modifies orbital J-cost and splits the 2S and 2P levels. J-cost is the derived cost of a recognition event, obtained from the comparator of a multiplicative recognizer on positive ratios. Upstream structures supply the ledger factorization that calibrates J and the spectral emergence that fixes the gauge content and three generations.
proof idea
One-line term-mode wrapper that unfolds the definition of the approximation and applies norm_num to discharge the concrete numerical inequality.
why it matters
This bound closes the size estimate for the Lamb shift in the RS QFT derivation, showing why vacuum J-cost fluctuations produce only a 1057 MHz correction. It supports sibling results that compute the shift frequency in MHz and the fractional correction. The result sits inside the alpha band of the forcing chain, where the inverse fine-structure constant is forced near 137.03.
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