nx_gsplat_fit_gate.nx

nx_gsplat_fit_gate.nx -- THE RECONSTRUCTOR TOOTH: can we FIT gaussians to an image, or only PLACE them? WHY THIS GATE EXISTS. Until 2026-08-23 nx_gsplat could optimise COLOUR only. Colour is the easy leg -- a pixel is LINEAR in colour, so the gradient is analytic and a step cannot really go wrong. Position is what 3D Gaussian Splatting actually IS: without it we have a splat RENDERER, not a splat RECONSTRUCTOR, and the whole photoreal-avatar lane rests on reconstruction. gs_pos_grad_step adds the position leg. ★★THE ACCEPT RULE IS DECLARED HERE, BEFORE THE EXPERIMENT, and it is deliberately threshold-free: MONOTONE RECOVERY -- the mean |position - truth| must STRICTLY DECREASE at EVERY step. Not "drops below X", which is a number nobody measured; strict monotonicity over the whole run. This is the ANTI-VACUITY tooth and it is the reason the gate exists: - an implementation whose position gradient is ZERO leaves the error EXACTLY constant -> FAILS - an implementation that JITTERS reduces error sometimes and raises it others -> FAILS - only a gradient that actually points downhill can decrease it every single step. A loss-only tooth would pass all three, which is why loss is reported but is NOT the accept rule. ★AND THE OPTIMUM IS A CONTROL, NOT AN ASSUMPTION. T5 runs the SAME step on a scene ALREADY at truth. A correct gradient is ~0 there and the scene must stay put; a jittering one wanders. The bite is asked both directions -- fires on the perturbed scene, silent on the converged one -- because a step that moves everything passes every "it moved" check ever written. ⚠FIXTURE HONOURS THE DECLARED APPROXIMATION. gs_pos_grad_step ignores transmittance (stated in its own header), so the fixture separates every gaussian in DEPTH: the approximation is exact for a non-overlapping scene, and testing an organ outside its declared domain measures the fixture. license_tier: ORIGINAL expect_exit: 0