Baguette: the vocabulary objective in two row halves fits the logit plane and computes the same rows

Baguette's training objective (tied vocabulary product, target gather, exact loss rows, exact logit gradient) is row-wise: each output row depends only on its own input row. On the RTX 3070 the recomputed realization runs it in two halves of h = 2048 rows each. Its logit plane holds 4*(2h)V bytes of binary32 logits (V = 65536 vocabulary entries). One half's binary32 logits take the plane's first 4hV bytes, and the whole bfloat16 logit gradient (2(2h)V bytes) takes the rest. This statement shows three things. (1) The gradient, starting at L + 4hV, ends exactly at the plane's end L + 4(2h)V. (2) Evaluating a row-wise function half by half (rows i < h in the first half, rows h + j in the second) gives the same value for every row i < 2h. (3) One row's row maxima, 4(V/128) bytes, fit inside that row's 2V bytes of gradient, so each half's maxima can sit at the start of its own gradient rows. The binary32 gradient bank then no longer hosts the logit gradient, freeing gradient slices 0..37 for attention-state slots of layers 1..38. That removes another 114 launches of forward replay per update with bit-identical checkpoints.