nx_autograd_tensor.nx

nx_autograd_tensor.nx -- TRAIN-R2 (T6): TENSOR reverse-mode autograd -- the identities that scale. Rung-1's tape held scalars; real models hold ARRAYS. Same tape shape, now stride-7: {op, ai, bi, rows, cols, valp, gradp} -- valp/gradp index a per-build BUMP ARENA of f32 cells (st[1] counter; no allocator, no fragmentation, deterministic). Forward EAGER, backward ONE reverse sweep. Four backward identities (learn these and every architecture MLP->transformer->DiT is composition): 1. matvec y=W*x (W r*c, x c): dW[i][j] += gy[i]*x[j] (outer product); dx[j] += sum_i W[i][j]*gy[i] (W^T gy) 2. vadd y=x+b: both inputs receive gy unchanged (bias gradients are free) 3. relu elementwise: pass gy[i] iff the INPUT cell was > 0 4. mse L=(1/n)sum(p-t)^2: dp_i += gL*(2/n)*(p_i - t_i); target grad nobody reads Scalar ops (sum, average) compose for free: matvec(1x1, 1x1) = scalar multiply, vadd of 1-cell nodes = add. genealogy_id: linnainmaa_1970_reverse_mode_ad + the matmul-backward identity (dA=dC B^T, dB=A^T dC) lineage_id: sovereign_tensor_tape_autograd_v1 license_tier: ORIGINAL verdict: GREEN (nx_train_r2_gate 2026-06-14: MLP gradcheck + affine-recover + bit-exact + AdamW)