Record the exact composition, and the seed it stops one step short of

`45a7176` composes a box down its move chain on a grid fine enough to round
once instead of once a level. `Holds::through`'s two-route allowance is two
half steps where it was three, and it cost nothing: 1,880M instructions and
755M cycles against 1,908M and 760M, with all twenty-five work counters
identical. What paid for the widening is that a length composes on its own in
half the multiplies both ends of a box need, and that only the fraction needs
the extra room.

The i64 item in "Next" keeps the measurement that redirected it, since
aiming the work at the screen invariant would have been wasted.

One half step further is arithmetically available and not taken: shrinker
seed 220 on `reorder` then diverges warm against cold, by re-breaking a
wrapping text whose reported width moves a `Branch` onto its other subtree.
That is written up under the `Holds::through` invariant with its reduction
command and its ten-widget tree, and it is the next thing to chase.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

docs/HANDOFF.md

@@ -8,7 +8,7 @@ log.
 
 Canonical Iris `main` is **`ca2b4b2`** (#17, the headless rig). **#18
 `split/18-position-chain`** is open in `/home/bob/repos/iris-pr18`; its local
-head is **`d21a215`**, eighty commits, pushed. Built-in alignment is
+head is **`45a7176`**, eighty-one commits, pushed. Built-in alignment is
 complete there; see "Built-in alignment" below for the retained-layout
 details. No PR reviews were present when checked on 2026-09-15.
 
@@ -167,15 +167,16 @@ in, and it is compiled out of the release runs above.
 
 ## Verification
 
-**At `e166e00`**, the current head:
+**At `45a7176`**, the current head:
 
 - `cargo fmt --all --check`, `cargo clippy --workspace --all-targets --
   -D warnings`, `cargo test --workspace`: sixteen targets green, 83 suite
   tests, 17 core unit tests, 11 generated cases. What stays ignored is the
   long runs and the profiling rigs; no known defect is ignored any more.
 - The release oracle at 100 seeds in 14.3 s, **all fifteen shrinker cases at
-  400 seeds of depth 5** in 57 s, and **1000 seeds of depth 6** in 145 s. The
-  last two pass for the first time.
+  400 seeds of depth 5** in 57 s, and **1000 seeds of depth 6** in 143 s. The
+  last two pass for the first time, and have kept passing across every
+  commit since.
 - `view`, `minimal` and `random` render byte-identical at 1920x1200 against
   `98d4e98`. `tabs` and `text` changed twice on purpose: `08c9d5a` moved an
   antialiased edge by less than a pixel (see "Performance") and `2bc6bdf`
@@ -758,10 +759,29 @@ pixels and `Holds`. Decided with Bryan on 2026-09-15.
   point that need not contain the box the part was drawn in. What it allows
   for has two parts and they are not the same shape.
   - **The two routes to a length** -- composed down the chain against
-    measured against the window -- get three half steps either side. That is
-    the floor: two fires the `Holds` assertion on eleven generated cases.
-    Four was tried and was overshoot, and tightening it moved none of the
-    rig's twenty-five work counters, so slack here buys no reuse (`38eba54`).
+    measured against the window -- get two half steps either side, since
+    `45a7176` made the walk round once instead of once a level. It was three
+    while composing rounded per level, and four before that, which was
+    overshoot. Tightening it has never moved one of the rig's twenty-five
+    work counters, so slack here buys no reuse.
+
+    **One half step further is arithmetically available and deliberately not
+    taken.** The `Holds` assertion is quiet at one, and the whole-of-a-box
+    case becomes an exact identity. What stops it is shrinker seed 220 on
+    `reorder`, which then lays out differently warm than cold: too narrow a
+    range is supposed to cost a redraw and nothing else, and there it
+    re-breaks a wrapping text, whose reported width moves a `Branch` onto
+    its other subtree. **That is the next thing to chase** -- it is the
+    unsettled-text family rather than a rounding question, it reduces to ten
+    widgets, and closing it is what lets this go lower:
+
+    ```sh
+    SHRINK_SEED=220 SHRINK_DEPTH=5 SHRINK_CASE=reorder \
+      cargo test --release --test shrink -- --ignored --nocapture
+    ```
+
+    The tree is `Scroll(X) { Pad as a region node { Span(X) { Branch,
+    Span(X){ wrapped text, one-line text } } } }`.
   - **The multiply on the way in** gets one more step at the top of the range
     and nothing at the bottom, since truncation only ever drops. The whole of
     a box has no multiply in it, however many pixels are added to it, and
@@ -954,9 +974,10 @@ Queued from this work, in order:
   since `a8898aa`. Still awaiting Bryan: whether a `Max` narrows the box the
   child draws in, or only what the parent reports for it.
 
-- **Compose in `i64` and narrow only when storing** (Bryan, 2026-09-16).
-  Chosen for the share spread; **what it buys is not that**, found on
-  2026-09-16 and worth reading before starting.
+- ~~**Compose in `i64` and narrow only when storing**~~ -- **done in
+  `45a7176`**, and what it bought is below. The rest of this item is kept
+  because the measurement in it is what stopped the work being aimed at the
+  wrong thing.
 
   The range inside a single operation is already protected -- `Fixed::mul`
   widens to `i64` for the product, `Holds::through` does all of its
@@ -986,19 +1007,20 @@ Queued from this work, in order:
   pushes a value across the `floor` -- which is what moved `tabs`'s corner
   arcs by a pixel at `08c9d5a`.
 
-  What is left to buy is **layout's own decisions**, which is not nothing:
-  the `Span` leftover boundary and the clamp crossover are structural
-  decisions taken on a pixel comparison, `Holds` validity is a pixel
-  interval, and warm-against-cold agreement is the thing every rig here
-  measures. The success test is `Holds::through`'s two-route allowance
-  shrinking from three half steps toward zero, in debug where the assertion
-  is live.
+  What it bought is **layout's own decisions**: `Holds::through`'s two-route
+  allowance went from three half steps to two, and the whole of a box now
+  maps back to one step rather than one step per level of nesting.
 
-  Two things to decide before starting: how many fractional bits the
-  intermediate keeps, since chained multiplies accumulate them and an `i64`
-  runs out too; and whether it keeps `UiSpan::within` inside the inliner,
-  which is what actually moves cycles there -- a `Wide` that makes the body
-  bigger loses on the axis the truncating multiply won on.
+  **And it was free.** 1,880M instructions and 755M cycles against 1,908M
+  and 760M, medians of 25 with all twenty-five work counters identical.
+  Two things paid for the widening and are the reason to keep them: a
+  *length* composes on its own in two multiplies a level rather than the
+  four both ends cost, since where the parent sits falls out of the
+  difference; and the pixel term takes its fraction on the ordinary grid, so
+  only the fraction itself -- the part that compounds multiplicatively --
+  needs the room. A third, skipping a parent that spans its own box, cost
+  18M instructions and is not there, the same verdict `UiSpan::within`'s
+  short-circuits got.
 
 Other queued work, in dependency order: