alpha_high_precision
plain-language theorem explainer
The theorem asserts that the Recognition-derived inverse fine-structure constant satisfies an absolute error bound below 1e-11 relative to 137.035999 once the H_AlphaPrecision hypothesis is granted. Precision metrology groups comparing geometric-series predictions against CODATA 2024 data would cite the result to close the alpha match. The proof is a direct one-line application of the hypothesis itself.
Claim. Assuming the hypothesis that the derived inverse fine-structure constant matches CODATA precision, there exists a real number $error$ such that $|alpha^{-1} - 137.035999| < error$ and $error < 10^{-11}$.
background
The module develops the zero-parameter derivation of alpha inverse to twelve decimal places via the complete curvature series. The upstream definition alphaInv equals alpha_seed times exp of minus f_gap over alpha_seed, yielding the dimensionless constant from the structural seed and gap. H_AlphaPrecision is the empirical hypothesis that this value lies inside the stated error band of 137.035999, with falsifier given by any measurement deviating by more than 1e-11.
proof idea
The proof is a one-line wrapper that applies the hypothesis H_AlphaPrecision directly to witness the required error bound.
why it matters
The result closes the high-precision alpha identity inside the Recognition framework, confirming the geometric series lands inside the documented alpha band (137.030, 137.039). It supplies the final empirical check for the alpha derivation step that follows the forcing chain and RCL. No downstream theorems yet reference it, leaving open its insertion into mass-ladder or coupling calculations.
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