nx_ng_diffrender.nx

nx_ng_diffrender.nx -- CAP-DIFF-RENDER, the next missing generation past the sovereign-raster substrate (nx_ng_gap: prereqs CAP-RASTER + CAP-NF-AUTOGRAD BUILT -> this is the adjacent-possible build). The FIRST rung of differentiable rendering: gradients of rendered PIXELS w.r.t. a SCENE PARAMETER, the substrate NeRF / 3D-Gaussian-Splatting optimization is built on. Minimal honest proof (operator: measured, no wave; HARD evidence per the genealogy ladder): a 1D soft-edge rasterizer renders an image from one scene param p (the edge position) in Q16 fixed-point. We then OPTIMIZE p by gradient descent to match a target image (rendered at p*). Correctness is proven the rigorous way: T1 DESCENT converges -- GD on p drives loss -> ~0 and p -> p* (the gradient points the right way), T2 NEG-CONTROL diverges -- ASCENDING the same gradient INCREASES loss (the gradient has teeth/direction), T3 finite-difference SIGN check -- sign(analytic dLoss/dp) == sign((L(p+e)-L(p-e))) (the gradient is real), T4 zero-at-optimum -- loss(p*) == 0 (the render + loss are consistent). Q16 fixed-point only (no float), sovereign syscalls only. license_tier: ORIGINAL expect_exit: 0