c_SI_pos

The SI Bridge Closure module fixes the unique conversion map from RS-native units to SI once a dimensional anchor is supplied. In native units the framework predicts $c_{\mathrm{RS}} = 1$, $\hbar_{\mathrm{RS}} = \varphi^{-5}$, $G_{\mathrm{RS}} = \varphi^5/\pi$. The bridge is three positive factors $a_T$ (sec/tick), $a_L$ (m/voxel), $a_M$ (kg/cohmass) matched to SI via the c, $\hbar$, and $G$ constraints.

Under SI-2019, $c_{\mathrm{SI}}$ is an exact definitional constant, not a measurement. This module (and sibling ExternalAnchors / SIConversion modules) bind that constant as the real $299792458$. Positivity of $c_{\mathrm{SI}}$ is the elementary gate for every later division or power that appears in the calibration identities, notably $a_T^2 = \pi , \hbar_{\mathrm{SI}} G_{\mathrm{SI}} / c_{\mathrm{SI}}^5$.

One-line tactic proof: unfold the local definition of $c_{\mathrm{SI}}$ to the literal $299792458$, then norm_num closes $0 < 299792458$. No lemmas are invoked beyond the definition itself.

This is the positivity hinge for the SI bridge uniqueness chain. Downstream it is used by a_T_sq_eq (the main closed form $\tau_0 = \sqrt{\pi},\tau_{\mathrm{Planck}}$), by aM_aT_eq_of_c_hbar and aT_aM_eq_of_c_G (which rearrange the c+$\hbar$ and c+$G$ constraints), and by tau_Planck_pos. Outside the module it feeds calibratedTickSquare_pos and calibratedTickSquare_injective in NativeDimensionalBoundary, which show that any positive supplied $G$ yields a positive tick square and that the bridge depends injectively on that anchor.

In the broader Recognition picture this sits at the dimensional-bridge layer: RS predicts the dimensionless triple $(c,\hbar,G)$ in native units; the SI map is uniquely fixed once $G_{\mathrm{SI}}$ is anchored. The theorem does not touch T5–T8 or the RCL; it is pure SI bookkeeping required for the closure status of the conversion map.