nx_autograd.nx

nx_autograd.nx -- TRAIN-R1: scalar tape-based reverse-mode autograd. THE training keystone: once gradients are correct and an optimizer drives a loss down, every model the team trains (the FNet text model, the pixel engine) is the SAME loop at larger scale. Inference is already sovereign; this is the missing BACKWARD half. Spec: knowledge/specs/2026-06-09-tutoring-training-substrate-rung1.md. TAPE: stride-5 nodes {op, ai, bi, val, grad} in one i64 array. Construction is EAGER -- creating a node computes its f32 `val` via the EXISTING nx_f32 ops (reuse, never reimplement). Backward = ONE reverse sweep (nodes are built in topological order, so reverse order visits parents before children) accumulating into `grad`: add: g->both | mul: ga+=g*vb, gb+=g*va | sub: ga+=g, gb+=-g | relu: pass g iff input val>0. Seed grad[root]=1.0. The whole engine is ~50 lines BECAUSE the f32 numeric tower already exists. genealogy_id: linnainmaa_1970_reverse_mode_ad + rumelhart_1986_backprop lineage_id: sovereign_scalar_tape_autograd_v1 license_tier: ORIGINAL verdict: GREEN (nx_train_r1_gate 2026-06-14: gradcheck + model-learns + bit-exact)