docs(perf): record the k-split negative result and correct §16's proposed fix

[justinchuby]

Docs-only. Closes out the hypothesis §16 named, with the evidence, after an adversarial review corrected both tallies and the scope of the conclusion.

Result

36 cells (6 llama/qwen shapes × t=1,2,4,8,16,32), 3 reps, two prebuilt test binaries alternated, portable drift control 0.999, t=1 rows as an identical-code null control.

That control fails on 1x1024x3072 (−29% in one matrix, +14% in the other, on code that is identical at one thread), so all five of that shape's cells are dropped — its wins and its losses — leaving 25 counted cells:

• v1 hybrid band × column, serial reduction: 8 wins, 5 losses, 12 neutral, geomean 0.997 — a wash. And it inverts its own prediction: the gain should grow with thread count as the stripe narrows; t=4 is the best column and t=32 the worst.
• v2 pool-aligned bands + parallel reduction (the Amdahl fix, bands*threads/k ≈ 6%): 3 wins, 13 losses, 9 neutral, geomean 0.846 (3/12/9, 0.904 with one unexplained 0.17x cell also excluded).

A second parallel plan, a scratch allocation and a reduction have to earn their place. 0.997 does not buy them. Code #1617 is closed unmerged.

Kept on the record

Accumulation is wrapping i32, so summing bands in band order is bit-identical to one pass — a k split owes an equality, not a tolerance. Asserted at every thread count; both plan gates mutation-checked.

Scope, stated narrowly

The experiment moved two things at once — the access pattern and the addition of scratch — and the scratch is the best explanation of the v2 result. So the streaming layout was never measured in isolation, and this does not rule out prepacked/reordered B, huge pages, software prefetch, NUMA first-touch, or gating the split to only the sub-page-stripe case.

The "instruction-bound inside L3" reading rests on §16's aspect-ratio sweep, not on this — a confounded A/B corroborates, it does not independently confirm. The planning consequence is a priority call, not a proof that layout work is dead: the instruction budget is the measured term (vpmaddwd at ~0.31 total uops/byte of B, ~0.25 vector-only), so paths cutting bytes and uops per weight together — the packed-nibble int4 kernel at 0.5 B/weight — are the better next spend.

Docs-only: no code, no test or CI gate reads these files.