Cumulative S/N forecasts for detecting the gravitomagnetic lensing signal as a function of maximum angular multipole, ℓ. All forecasts assume a sky fraction of f_sky ≈ 0.25. Left: S/N for the cross-correlation of the lensing convergence with the reconstructed momentum convergence field for different galaxy number densities (${\overline{n}}_g$, in units of Mpc⁻³); solid lines show cosmic-variance-limited lensing noise, while dashed lines show stage-four lensing survey noise. Middle: Cosmic-variance-limited S/N for three different momentum field tracers: the true, noiseless field (κ_j)∥); the reconstructed field (${\widehat{\kappa }}_{j)\Vert }$), assuming a galaxy density of ${\overline{n}}_g={10}^{-2}$ Mpc⁻³; and the kinetic Sunyaev-Zel’dovich (kSZ) effect. Right: S/N for the cross-correlation after subtracting a reconstructed density convergence field (${\widehat{\kappa }}_{\varphi }$), where the different lines show the effect of varying the galaxy density used for the density reconstruction.