G_RS

The SI Bridge Closure module fixes the unique calibration map from RS-native units to SI. In the native gauge the framework predicts the dimensionless triple $c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^{5}/\pi$, together with the recognition/Planck identity $G\cdot\pi\cdot\hbar=\lambda_{\mathrm{rec}}^{2}\cdot c^{3}$ at $\lambda_{\mathrm{rec}}=\ell_{0}=1$.

Three positive conversion factors $a_T$ (sec/tick), $a_L$ (m/voxel), $a_M$ (kg/cohmass) are constrained by matching those RS predictions to the SI values of $c$, $\hbar$, and $G$. Under SI-2019, $c_{\mathrm{SI}}$ and $\hbar_{\mathrm{SI}}$ are exact; $G_{\mathrm{SI}}$ is the CODATA anchor.

Upstream, the Physics module already records the same native value $G=\varphi^{5}/\pi$ (via the coherence exponent). The present definition re-exports that constant for the bridge algebra.

Pure definition: unfold to $\varphi^{5}/\pi$. No tactics. The algebraic content is the substitution $\lambda_{\mathrm{rec}}=c=1$, $\hbar=\varphi^{-5}$ into $G=\lambda_{\mathrm{rec}}^{2}c^{3}/(\pi\hbar)$, which cancels to $\varphi^{5}/\pi$.

This constant is the G-leg of the native triple that closes the SI conversion map. Downstream it appears in the G-constraint, positivity $G>0$, and the native Planck product $\hbar\cdot G=1/\pi$. Those feed the helper identities $a_M a_T$ and $a_T/a_M$, which multiply to the main algebraic result $a_T^{2}=\pi,\hbar_{\mathrm{SI}}G_{\mathrm{SI}}/c_{\mathrm{SI}}^{5}$ (i.e. $\tau_{0}=\sqrt{\pi},\tau_{\mathrm{Planck}}$). It is also used by the Einstein-relation lemma in the Planck-constant module and by the bridge certificate. Framework landmark: the primer value $G=\varphi^{5}/\pi$ in RS-native units.