nx_train_r1_gate.nx

nx_train_r1_gate.nx -- GATE for TRAIN-R1: the scalar-tape autograd keystone. Proves, by RUNNING, that the team can TRAIN a model sovereignly. Three exact gates (spec 2026-06-09-tutoring-training-substrate-rung1.md): 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). For each param: analytic grad (reverse-mode backward) vs central finite difference (f(p+h)-f(p-h))/2h, h=1/128; relative error < 1/32 (floor 1/64). Catches every sign/chain-rule defect a wrong autograd could ship. B A MODEL PROVABLY LEARNS: fit y = 1.5x - 0.5 (8 points x=i/4, targets in-f32) by full-batch gradient descent, lr=1/20, 500 epochs, MSE via the tape. Assert final loss < 1/1000 AND |w-1.5| < 1/16 AND |b+0.5| < 1/16 AND final loss < first loss. The smallest EXACT statement of "we can train a model". C BIT-EXACT REPRODUCIBLE: run the whole training twice from zero-init; assert the final (w,b) f32 BITS are identical. GPU training is non-deterministic by default; the bits-up f32 substrate makes byte-identical training a GATE -- the determinism exceed-axis carried into ML. Evidence -> knowledge/status/train_r1.log (TRAINR1GATE authored=organ ... verdict=GREEN). license_tier: ORIGINAL