If dark matter halos have toroidal rather than spherical geometry, weak gravitational lensing around galaxies should exhibit an annular convergence ring at the torus major radius (Rmaj ≈ 100 kpc) — a signal that no spherically symmetric mass distribution can produce. We present a quantitative prediction for this signal and three independent tests using existing survey data: (i) face-on galaxy stacking (b/a > 0. 8) should reveal an annular excess at R ≈ 100 kpc after NFW subtraction, detectable at raw 5σ with ∼7, 046–9, 981 face-on lenses from KiDS-1000 or DES-Y3 (post-look-elsewhere 5σ under Bonferroni T = 72 requires ∼9, 442–13, 374, the 1. 34× inflation factor; Edri 2026b, Table 6) ; (ii) standard NFW fits to any stacked galaxy-galaxy lensing profile should show systematic negative excess surface mass density (ΔΣ < 0) at R ∼ 50–90 kpc, a signature impossible for monotonically decreasing profiles; (iii) NFW halo masses recovered from face-on galaxy stacks should be systematically lower than from edge-on stacks of matched true mass. If no annular residual is found across R ∈ 50, 200 kpc in ∼7, 046 face-on KiDS-1000 galaxies under a template scan over Rmajᵗmpl (and, jointly, no γt sign change or negative-ΔΣ signature in mass-binned stacks), the toroidal halo geometry is falsified; a null only at the pre-registered Rmaj = 100 kpc anchor does not suffice, as it is degenerate with a systematic error in the rotation-curve-calibrated Rmaj. All three tests require no new observations — only reanalysis of existing public data.
Avi Edri (Mon,) studied this question.