nx_train_r3_gate.nx

nx_train_r3_gate.nx -- GATE for TRAIN-R3 (T7): softmax + cross-entropy + nonlinear training. Proves, by RUNNING: A GRADCHECK the new ops: softmax-cross-entropy (dlogits = softmax - onehot) AND standalone softmax (Jacobian-vector product), analytic vs central finite difference (h=1/128, rel<1/32 floor 1/64). B TRAIN A NONLINEAR CLASSIFIER -- XOR: a 2->8(relu)->2 MLP with a softmax-CE head and a DETERMINISTIC symmetry-breaking init, trained by AdamW. XOR is the canonical proof that a LINEAR model CANNOT solve it -- reaching 4/4 correct demonstrates real nonlinear learning. Assert accuracy==4 AND loss decreased. C BIT-EXACT: train twice from the same init -> identical final bits for all 42 parameters. Evidence -> knowledge/status/train_r3.log (TRAINR3GATE authored=organ ... verdict=GREEN). license_tier: ORIGINAL