We show that excising tetrahedra from a Regge triangulation concentrates all curvatureat the void boundary - none remains in the interior (f∂ = 1.000 to ∼10−12) - andthat the Gauss-Bonnet theorem uniquely selects toroidal topology (χ = 0) as the onlycosmologically viable void shape, by twelve orders of magnitude (α ∼ 109). This geometricmechanism requires no dark matter particles and no modified gravity: the curvature budgetof a toroidal void in discrete spacetime, governed by the same GaussBonnet theorem thatconstrains smooth manifolds, provides a complete gravitational potential equivalent to adark matter halo.The curvature balance C+ = C− is conrmed by Richardson extrapolation on sharptoroidal voids (N = 5,000-320,000, 10 seeds per resolution): continuum limit |O∞| = 1.026±0.113 (95% CI 0.913, 1.139, R2 = 0.998). The Regge action difference ΔSR < 0 at all voidradii with 100% sign consistency across 80 realizations, establishing that voids are lower-action states. SPARC calibration yields the physical void scale (ℓ = 5.0 kpc, Rmaj =100 kpc, Rmin = 20 kpc), and a BIC comparison on 171 SPARC galaxies finds the voidmodel preferred over NFW (90 vs. 69 galaxies at equal parameter count k = 2). A 58-testverification suite (50 pass, 6 caveats, 2 fail) provides independent numerical confirmation.The Hopf link-breaking experiment confirms ΔC = 4πΔχ in the discrete setting to |ε| <10−6.
Avi Edri (Thu,) studied this question.