We present the Topological String-Gradient Theory (TSGT), a framework in which space-time is discrete at the Planck scale and gravity is the gradient of the spacing between discreteelements ("pixels"). Two kinematic postulates—a spatial pixel strain set by the Newtonianpotential and an equal temporal strain—reproduce the weak-field Schwarzschild metric, in-cluding the full light deflection ∆θ = 4GM/c2b; this reproduction is by construction. The dis-crete substrate is a random Poisson sprinkling of density L−4p , which preserves Lorentz invari-ance statistically and removes the preferred-frame problems of lattice formulations; lattice-derived predictions of earlier versions are retracted. If cosmic expansion creates new pixelsrather than stretching existing ones—the only option compatible with an invariant Lp—thenPoisson fluctuations in the pixel count fix the cosmological term to ρΛ ≃ 2.8 × 10−27 kg m−3,within a factor of two of the observed value; this argument is Sorkin’s heuristic, followinghere from TSGT’s own postulates. Written locally, the number—volume correspondence isthe unimodular constraint; enforcing it in an Einstein—Hilbert action yields the trace-freeEinstein equations, making TSGT provably equivalent to General Relativity at the classicallevel. The framework’s independent content lies in the integer character of the pixel countand in the fluctuating dark-energy term it implies (w̸ = −1). Unresolved problems, includingthe absence of a dynamical equation for the pixel density, are listed explicitly.