nx_ng_volrender.nx

nx_ng_volrender.nx -- CAP-VOLUME-RENDER, generation 7 on the neural-graphics ladder (nx_ng_gap named it the next missing generation after CAP-DIFF-RENDER). The volumetric ALPHA-OVER compositing operator that is the actual render op of NeRF (after the density->alpha map) AND the core of 3D Gaussian Splatting: T_0 = 1 ; C = sum_i T_i * alpha_i * c_i ; T_{i+1} = T_i * (1 - alpha_i) i.e. front-to-back "over" compositing along a ray. Q16 fixed-point, no float, sovereign syscalls only. Honest gated proof (HARD evidence per the genealogy ladder): T1 FORWARD correctness -- opaque front occludes the rest (C==c0); all-transparent shows background (C==0); half-opaque samples composite to the hand-checked weighted sum (transmittance chain is right). T2 DIFFERENTIABLE -- the per-sample compositing weight w_i = T_i*alpha_i IS dC/dc_i; GD on the sample colors drives the composited C -> a target C*, loss -> ~0 (gradients flow through the render). T3 NEG-CONTROL -- ascending that gradient DIVERGES (the gradient has correct direction/teeth). T4 GRADCHECK -- sign(analytic dLoss/dc0) == sign(L(c0+e)-L(c0-e)). NOTE: the NeRF density form alpha=1-exp(-sigma*delta) is a thin wrapper over this (exp helper already in nx_nofloat_autograd); the alpha/sigma gradient is the follow-on rung. license_tier: ORIGINAL expect_exit: 0