gravitational_constant_precision
plain-language theorem explainer
The declaration establishes that the Recognition Science derivation of Newton's gravitational constant G agrees with the CODATA 2018 value to within 22 parts per million, provided the Planck gate identity hypothesis holds. Researchers comparing fundamental constants to experimental data would reference this result. The proof consists of a direct invocation of the hypothesis H_GPrecision.
Claim. Assuming the Planck gate identity hypothesis $H_{GPrecision}$, there exists a real number $error$ such that $|G - 6.67430e-11| < error$ and $error < 1e-15$, where $G = lambda_rec^2 c^3 / (pi hbar)$ is the derived gravitational constant.
background
This module addresses Phase 12.3 of the Recognition Science framework: deriving the gravitational constant to six or more significant figures from the Planck gate identity. The derived $G$ takes the form $G = lambda_rec^2 c^3 / (pi hbar)$ in RS-native units with $c=1$ and $hbar = phi^{-5}$. The sibling definition $H_GPrecision$ encodes the empirical claim that this expression matches the CODATA 2018 value 6.67430e-11 within an error bound below $1e-15$ (corresponding to 22 ppm). Upstream results supply the explicit formula for $G$ in Constants and the numerical CODATA target; the J-cost and functional-equation reparametrizations supply the log-coordinate structure underlying the derivation.
proof idea
The proof is a one-line wrapper that directly applies the hypothesis H_GPrecision.
why it matters
This theorem supplies the high-precision numerical match for G required by the Recognition Science constants pipeline, closing the Phase 12.3 claim that the derived value lies within 22 ppm of experiment. It sits downstream of the Planck-gate derivation of G and the CODATA definition, and it supports any later precision test of the framework against measured constants. No downstream uses are recorded, leaving open whether the same precision statement will be invoked in mass-ladder or alpha-band calculations.
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