cpAngle

The module derives the Jarlskog invariant $J_{\mathrm{CP}}$ (the unique rephasing-invariant measure of quark-sector CP violation) from Recognition Science geometry: torsion gaps, flip-count asymmetry, and a Berry-phase CP angle. In the Wolfenstein form one has $J\approx A^2\lambda^6\sin\delta$; the structural RS inputs fix $A$ from the torsion ratio $6/11$, $\lambda$ from the gap $\Delta\tau_{12}=11$ and flip ratio $4:2$, and $\delta$ from the generation Berry phases.

Eight-tick phases supply the elementary angles $k\pi/4$ for $k=0,\ldots,7$. The raw CP phase (imported from the CP-phase derivation) is the difference of per-cycle Berry phases on the first two generations, which evaluates to $4\cdot(\pi/4)-2\cdot(\pi/4)=\pi/2$. This definition simply names that real number $\delta$ for use in the Jarlskog formulae.

One-line definitional alias: cpAngle is set equal to the upstream raw CP phase. No tactics or lemmas are invoked; the numerical content $\delta=\pi/2$ is inherited from the Berry-phase difference already computed in the CP-phase derivation module.

This is the single named real that carries the CP angle into the Jarlskog sector. Downstream, the structural invariant is $J_{\mathrm{struct}}=A^2\lambda^6\sin(\delta)$ with this $\delta$; positivity of $J$, the certificate fields sin_cp_nonzero and cp_exists, and the small-but-nonzero theorem all unfold through it. The module claims maximal per-cycle CP violation: $\sin(\delta)=\sin(\pi/2)=1$, so the observed smallness of $J$ comes entirely from $\phi$-suppressed $\lambda^6$, not from a tuned phase. That matches the RS story linking eight-tick geometry (T7) and cube-derived CKM angles to the measured $J\sim 3\times 10^{-5}$.