hop_cached_vs_gather: the scatter is O(N/64 + selected bits) per facet, not O(frontier)

CodeRabbit on #79: scatter walks every word of selected before visiting
set bits — 1 024 words per facet at 65 536 rows regardless of frontier
size. Doc and board entry corrected; implementation unchanged.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01DCfrD5y19cvFc4AoyydXYv

Author: claude

.claude/board/LATEST_STATE.md

@@ -30,8 +30,10 @@ Cache build: **843–930 µs**.
 - **The tile pays for itself on the second hop at every frontier.** A store
   generation's predicates do not change between hops; the shipped body
   re-derives them with 64 contiguous 256 KiB passes per hop. With the tile,
-  what is left is ≤ 5 µs of `mask_and` plus the scatter, which is O(frontier)
-  and the whole cost above ~1 %.
+  what is left is ≤ 5 µs of `mask_and` plus the scatter, which is
+  `O(N/64 + selected bits)` per facet (it walks every word of `selected`
+  before knowing which are empty — CodeRabbit on #79 corrected an
+  "O(frontier)" claim here) and the whole cost above ~1 %.
 - **Not measured here:** invalidation (a write to any classid/hi32 lane of the
   generation drops all 32 masks — the registry already does this wholesale for
   `cached_carving`), and the cache multiplies by the number of edge classes

native/lgj-abi/examples/hop_cached_vs_gather.rs

@@ -36,8 +36,11 @@
 //! hops at every frontier): a store generation's predicates do not change
 //! between hops, and the shipped body re-derives them with 64 contiguous
 //! 256 KiB passes per hop. What remains per hop is one 8 KiB `mask_and` per
-//! facet (≤ 5 µs) plus the scatter, which is O(frontier) and is the whole
-//! cost above ~1 %.
+//! facet (≤ 5 µs) plus the scatter, which is `O(N/64 + selected bits)` per
+//! facet — it walks every word of `selected` before it can know which are
+//! empty (the same word-walk floor `ternlogq_sparse_reapply_probe` measured,
+//! ~360 ns at 1 024 words), then one payload read per set bit — and is the
+//! whole cost above ~1 %.
 //!
 //! The `gather` column is NOT a competitor to the mask (R1 ruled the
 //! population serialization out); it is the baseline for the *access shape*