Record where a regroup's time actually goes

The §9 note said the scan was half a regroup and implied the
agglomeration was an irreducible sequential walk. Both halves of that
are now wrong, and the numbers are the point of the section.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

docs/faces.md

@@ -674,11 +674,26 @@ app builds for has it, and the explicit `vfmaq` matters because LLVM will not fu
 add on its own. The portable loop remains the definition the others are tested against. All three
 produce the same 1,531,969 pairs.
 
-Worth keeping in view when this is next optimised: on that library a full regroup is **scan 4.60 s ·
-agglomerate 4.84 s · score 0.23 s**, so the scan was under half of it and the SIMD work moved the
-whole pass from 10.0 s to 5.9 s. A GPU GEMM is the next step for the scan, and it is capped by the same
-arithmetic — the agglomeration is a sequential heap walk and no amount of silicon touches
-it.
+**Where a regroup's time actually goes**, on that library, because the answer moved twice while it
+was being looked at:
+
+| | before | after |
+|---|---|---|
+| scan | 4.60 s | **0.94 s** |
+| agglomerate | 4.84 s | **1.75 s** |
+| score | 0.23 s | 0.28 s |
+| **total** | **10.0 s** | **3.0 s** |
+
+The scan came down by the kernel work above. The agglomeration was not, as it looked, an irreducible
+sequential heap walk: 3.06 s of it was every component scanning the *whole* pair list for the pairs
+that were its own — 382 million set lookups to place 804,499 pairs — which the union-find can do in
+one pass while it is finding the components anyway. Another 0.54 s was `Engine::cross` computing dot
+products with the portable loop while the scan beside it used the machine's SIMD.
+
+A GPU GEMM is the obvious next step for the scan, and it should be judged against the second column
+rather than the first: the scan is now under a third of the pass on a desktop, so the ceiling there
+is a 1.5× regroup. On a tablet, where the CPU is several times slower and the GPU is not, the split
+is different and the case is stronger — which is a measurement nobody has taken yet.
 
 **Constraints, not just thresholds:**