nx_nofloat_autograd_gate.nx

nx_nofloat_autograd_gate.nx -- HARD-EVIDENCE gate for the NO-FLOAT (integer Q16) general autograd (nx_nofloat_autograd). Proves, by RUNNING in pure integer arithmetic, that the team can do general reverse-mode backprop + train a model WITHOUT any float -- the genuine missing generation on the no-float DeepMind ladder. Mirrors the proven nx_train_r1_gate evidence shape, but Q16-integer: A GRADCHECK (oracle = mathematics): loss = ( relu(w1*x+b1)*w2 + b2 )^2 at params OFF the relu kink (w1=2/3, b1=1/4, w2=3/2, b2=1/4, x=3/4, all Q16). For each param: analytic grad (the tape's reverse sweep) vs CENTRAL finite difference (L(p+h)-L(p-h))/2h, h=1/128, all in Q16. Relative error < 1/32 (floor 1/16). This exercises matvec + vadd + RELU + mse backward -> a GENERAL graph, not one layer. D THE GRADCHECK HAS TEETH (neg-control): negate one analytic grad and assert the SAME check now FAILS -- a wrong gradient is provably caught (so gate A is not vacuously passing). B A MODEL PROVABLY LEARNS: the EXACT task nx_nn_train solves (linear layer W[1x2], target W*=[1.0,-0.5] Q16, 4 samples), but trained by the GENERAL TAPE (matvec->mse summed, one reverse sweep, nfa_sgd) instead of a hand-coded analytic gradient. Assert SSE loss collapses >=95% AND both weights converge >=60% of the way to target with correct sign. The general autograd REPRODUCES the special trainer. C BIT-EXACT REPRODUCIBLE: train twice from zero; assert the final integer weights are IDENTICAL. Integer add is EXACTLY associative -> determinism is STRUCTURAL here (a stronger exceed-axis than the f32 tower, which is only reproducible because it pins one summation order). Evidence -> knowledge/status/nofloat_autograd.log. Sovereign: imports nx_nofloat_autograd (pure integer; NO nx_f32 anywhere in this organ's import graph) + nx_syscalls. license_tier: ORIGINAL expect_exit: 0