hbar_SI_pos

The SI Bridge Closure module fixes the unique conversion from RS-native units to SI once a dimensional anchor is supplied. In native units the framework predicts $c_{\mathrm{RS}}=1$, $\hbar_{\mathrm{RS}}=\varphi^{-5}$, $G_{\mathrm{RS}}=\varphi^5/\pi$. Matching against SI values of $c$, $\hbar$, and $G$ determines three positive conversion factors $a_T$, $a_L$, $a_M$.

Under SI-2019, $c_{\mathrm{SI}}$ and $\hbar_{\mathrm{SI}}$ are exact definitional constants; $G_{\mathrm{SI}}$ remains the single measured CODATA input. The local definition sets $\hbar_{\mathrm{SI}} := 1.054571817\times 10^{-34}$, matching the ExternalAnchors decimal. Positivity of this constant is a prerequisite for every square-root Planck quantity and for the calibrated-tick formulas $a_T^2 = \pi,\hbar_{\mathrm{SI}} G_{\mathrm{SI}}/c_{\mathrm{SI}}^5$.

One-line tactic proof: unfold the definition of the SI reduced Planck constant to the concrete positive decimal, then apply norm_num to obtain $0 < 1.054571817\times 10^{-34}$. No lemmas beyond the definition are required.

Feeds every SI Planck-scale positivity and injectivity argument that divides by or takes square roots of expressions involving $\hbar$. Downstream uses include tau_Planck_pos in this module, calibratedTickSquare_pos and calibratedTickSquare_injective on the native dimensional boundary, and the BlackHoleEchoesSI cluster (planckLength_SI_pos, planckTime_SI_pos, geometric identities). Without $0<\hbar_{\mathrm{SI}}$, the closed-form tick $\tau_0=\sqrt{\pi},\tau_{\mathrm{Planck}}$ and the uniqueness of the SI conversion map cannot be stated in $\mathbb{R}{>0}$. The result is pure SI bookkeeping; it does not derive $\hbar$ from Recognition Science (native $\hbar{\mathrm{RS}}=\varphi^{-5}$ is separate).