ai-app/docs/LAYOUT.md

# iris: one `draw` that records a size

A widget draws once and records its size on the `Painter`. Reading a child
`DrawResult::size()` records a retained size dependency; drawing the child
without reading that result does not make the parent's size depend on it.

§1, §2 and §3 have landed in Iris (#16 and #18). §4 to §6 and the density
section retain the rationale of the design but still name types that have
since been replaced; they are not an API reference. `docs/HANDOFF.md` is the
current transparent-frames work and its checks; `docs/LAYOUT_LOG.md` is what
the sessions doing that work found, kept until it lands. The sections at the
end of this file are durable design moved out of the handoff on 2026-09-18.

## Design

### UI ownership and frame access

`Ui` owns both the mutable widget-side `UiData` and the retained
`UiRenderState`. It dereferences to `UiData`, so resources expose one `Ui`
without adding a second layer to ordinary widget, text, and texture access.
The render state itself remains private. `Ui::render_state()` returns an owned
`RenderHandle`, whose only public operation is a shared `get()` guard over the
last completed frame. Owning the handle, rather than borrowing `Ui`, lets a
controller inspect retained ancestry while it mutates other resources.

`UiRsc::draw` is the mutation boundary: it clones the private handle, takes
the exclusive guard, and updates the render state with the `Rsc`. Event
dispatch holds a shared guard for the whole callback, so events and controller
methods can reuse the completed tree but cannot start a draw or observe a
partially updated one. Controller ancestry is walked directly through that
tree; the event manager still maintains its per-event active-widget index in
draw hooks so dispatch never has to scan every active widget.

### 1. The new `Widget` trait

```rust
pub trait Widget: Any {
    fn draw(&mut self, painter: &mut Painter) -> Size;

    fn size_hint(&self, axis: Axis) -> Option<Len> { None }
}
```

Two methods, not three: `on_resize` was proposed here and shipped, and §3
below replaced it with the `Holds` interval a widget declares while drawing.

A widget returns what it used of the box it was given. A child
draw returns a `DrawResult` that keeps the painter borrowed; calling `.size()`
on that result reads the child's retained size and records that the current
widget depends on it. Dropping the result without reading it draws the child
without making the parent's own size depend on the child's.

No `available` parameter: `Painter` already carries the region the parent
handed down (`Painter::region()`) and already exposes the pixel-resolved form
(`px_size()`) and the output surface size (`output_size()`). Passing it again
would be the same value under a second name. `desired_width`/`desired_height`
and `WidgetAxisFns::desired_len` are deleted outright — not
deprecated, not kept as a fallback — because a widget that implements both
`draw` and `desired_*` for the same thing is exactly the "two names for one
concept" the code rules call out, and it is what today's `Span::desired_ortho`
(as it was then) already complains about in its
own comment: "this literally copies draw so that the lengths are correctly
set in the context, which makes this slow and not cool." Folding sizing into
`draw` deletes that duplicate simulation, not just moves it.

`size_hint` is not a second layout pass. It is an optional exact answer for
an axis the widget declares without painter context or child access. A
lying hint fails a debug assertion when the widget is drawn.

### 2. O(1) subtree movement

A widget opts into one independently movable region with `.region_node()`, or
`Widgets::set_region_node` at runtime; `.scrollable()` sets it once as its
convenient default. A node holds a whole **box** -- a `UiRegion` in its parent
node's coordinates, `UiRegion::FULL` being the identity -- and each primitive
instance names the node it was drawn under. Moving a subtree through a node
writes one entry. A widget without the property shares the nearest ancestor's
node, and moving it remaps its retained primitive, mask and active regions
instead, stopping at any descendant node after rewriting that one entry.

A box rather than a translation, because a pixel-space offset would scale a
child that has to keep its pixel length; the fraction and the offset in a
`UiScalar` are what tell the two apart. The parent chain is what makes nested
movable subtrees work -- a swipeable row inside a scrolling list -- and a flat
table would rewrite the row whenever an ancestor moved, which is the
`O(subtree)` work this removes. `CHAIN_LIMIT` bounds the walk at 64 in both
Rust (`core/src/ui/mod.rs`) and WGSL, so a malformed cycle resolves the same
way on each side.

`Moves::resolve` performs the same walk on the CPU for hit testing,
accessibility and window-coordinate queries, and the shader's `resolve_move`
mirrors it. Coordinates cross as whole counts of `1/1024` px and `1/2^24` of
a box, which the shader decodes from constants the Rust side prepends: the
grid is stated once. Masks carry their own node and resolve it independently,
so a stationary viewport clips content that moves inside it.

Nodes follow `ActiveData`'s lifecycle. Removing one retires its entry only
after every descendant has migrated, since reusing the index sooner would
make an old parent look current. Changing the property redraws the subtree
once, to rebuild the coordinate boundary; it belongs to widget identity,
which is safe because a widget has one parent.

### 3. Resize scope

A resize is "the region a widget's parent offers it changes such that the
widget's draw might produce different output" -- as opposed to a move, which
by construction cannot. Two independent narrowings apply, and both are
measured properties of the code rather than new machinery:

**(a) A window resize does not, by itself, require touching most widgets.**
The shader recomputes every primitive's position from `window.dim` and the
primitive's stored fraction and offset every frame, already, on the GPU. A
widget laid out purely in those terms is therefore correct after a resize
with no CPU work at all.

What decides the rest is `Holds`, one interval of box lengths per axis:
*give this widget any box in here and it draws the same thing and reports the
same size*. A widget that never reads its box in pixels holds for every
length. Reading `Painter::px_len(axis)` or `px_size()` narrows the interval
to the length read, and `Painter::holds` is how a widget widens it again by
saying what its drawing actually depends on -- a greedy line break holds from
its longest line up to the width it was made at. A parent holds for whatever
keeps every child it asked about or drew inside its own range, each child's
interval translated into lengths of the parent's box.

This replaced `Widget::on_resize` and its `Scale`/`Redraw`/`Translate`
answers, which said the same thing per widget type and could not say *how
far*. There is no per-widget resize mode now: a widget that reads nothing is
never redrawn for a resize, one that reads its width is redrawn when its
width leaves the interval it declared, and the interval is the whole of the
statement. Do not restore `Translate`; a retained subtree that only moves is
remapped through the box chain of §2, exactly.

Lengths are whole counts of `1/1024` px, so "the box changed" is equality
rather than a tolerance: a change too small to reach the next step is not a
change, and one that reaches it is, however little of a pixel it is worth.

**(b) Size invalidation travels upward before drawing; drawing itself travels
only downward.** Every active widget retains the direct children whose size it
read through `DrawResult::size()` or `Painter::known_len`. `redraw_updates`
takes one id from the dirty set, follows only those dependency edges upward
and marks that path dirty, then redraws its highest already-dirty ancestor.
Drawing that ancestor consumes the marks of every dirty descendant it
reaches; the loop then takes whatever remains. Drawing never synchronously
invalidates or invokes a parent, so there is no layout recursion.

Dirty widgets settle deepest-first. `dirty_size_under` has been deleted;
settling consumes descendant marks bottom-up, so no clean retained answer can
hide an unsettled size dependency. An exact `size_hint` stops propagation when
both axes still equal the retained size; otherwise propagation is deliberately
conservative, since only a dependent ancestor can assign the final boxes.
This is a generic constraint rule, not a text exception. Wrapped text is
merely the common example: it reads width, so changing only height leaves its
answer valid.

### 4. Wrapped text, and "needs child height before choosing width"

**Wrapped text is not a special case any more; it already reads as one
draw.** `TextView::render` (`iris/src/widget/text/mod.rs:57-76`) already
does exactly what single-draw asks for: it reads `ctx.px_len(Axis::X)` as the
wrap width, shapes once, and memoizes the shaped layout keyed on that width
plus a changed-flag on the buffer and attrs (`:63-69`) — a second call with
the same width is a hash-map-style cache hit, not a re-shape. Under the new
trait this collapses `Text::draw`/`desired_width`/`desired_height`
(`text/mod.rs:133-147`, three functions) into one `Text::draw` that calls
`self.view.draw(painter)` once, which internally still calls `render`
once, hits its own cache, and returns the size it already computed. No
new caching is needed here; the two now-redundant call sites
(`desired_width`/`desired_height` each separately calling `render`) simply
disappear, which is a second `render` avoided per frame per text widget
that is being measured by a parent.

`Span` has no size-only pass. It first reads exact, context-free
`Widget::size_hint(axis)` values. It then draws unknown fixed children
forward from the current cursor, retaining what they paint. Once every
length is known, flexible space is allocated and `Painter::place` moves
each retained child into its final box. A child is redrawn only when that
box changes the size it was drawn for.

Hints are optional and affect cost, never correctness. `SetSize` can report
its declared axis without inspecting its child, which covers the important
`.height(rest())` case. A debug assertion compares every hint with the
eventual `draw` result. Widgets whose answer depends on shaping or on a
child return `None`.

### 5. Caching and invalidation

`Cache.size` (`core/src/ui/cache.rs`) is **deleted, not replaced with an
equivalent** — the thing it memoized (a `desired_width`/`desired_height`
answer, independent of drawing) no longer exists as a separate query, so
there is nothing left to cache at that layer. What already provides "an
unchanged subtree costs nothing" is the check `draw_inner` performs before
touching a widget at all (`render_state.rs:85-90`): if the widget is active,
its region is unchanged, and it is not marked dirty, `draw_inner` returns
immediately — no `Painter` constructed, no primitive touched, no shader
work beyond what the GPU already redraws from the unchanged instance
buffer. That check is kept exactly as it is; it is the caching mechanism,
and it already operates at (id, region) granularity, which subsumes "(id,
available size)" once size *is* what a region change means.

`ActiveData::size` stores the value the widget's `draw` returned.
This is what a parent placing the widget for a second
frame without redrawing it reads instead of recomputing — it replaces
`Cache.size`'s role of "answer a size question without a full draw" with
"read the size of the last actual draw." `ActiveData::size_deps`
stores the direct children whose `DrawResult::size()` or known length the
widget observed during that same draw; the next draw replaces the list, so a
dependency disappears as soon as the widget stops reading it. Both fields
have `ActiveData`'s existing lifecycle through `remove`/`remove_rec`.

Retained draw output uses two buffers per collection. A redraw clears and
fills the spare child, primitive, texture, and paint buffers while consuming
the current buffers for reuse, then swaps their roles. Stable redraws therefore
reuse vector capacity and move matching resource handles instead of allocating
new collections or changing resource reference counts each frame.

### 6. Rejected alternatives

- **A flat (non-chained) per-subtree offset table**, Iris's literal
  phrasing — rejected in §2 for breaking under nested independent moves
  (a swiped row inside a scrolling list). Costs nothing extra to avoid: the
  chain is the same mechanism with one more field.
- **Keeping `region_mut` recursion as the only move mechanism** — rejected
  as the steady-state path (O(primitives in subtree), exactly what a
  transcript scroll must not pay every frame) but kept for resize-shaped
  changes (§3) where the content's own region field, not an ancestor
  chain, is what has to change.
- **A general measurement API** — rejected because it walks the same nested
  tree again. The narrow `size_hint(axis)` contract is exact,
  context-free, and optional; it exists only for sizes a widget already
  declares itself.
- **Passing `available` as an explicit parameter to `draw`** (mirroring
  Masonry's `layout(&mut self, ctx, bc: &BoxConstraints) -> Size`, the
  yardstick per AGENTS.md) — rejected as redundant with `Painter::region()`,
  which already carries the same information into every widget that needs
  it; adding a parameter would just be a second route to a value already
  reachable, and would invite the two drifting apart.
- **Eagerly propagating a moved widget's delta into every descendant's own
  offset value** (rather than chaining and resolving in the shader) —
  rejected as O(descendant widgets), which is smaller than O(primitives)
  but still not O(1), and the shader-side chain costs nothing extra to get
  the better bound.

## Density: `Len::dp`, resolved at `apply_rest` time

Iris asked for a third length kind beside `abs` (physical pixels) and
`rel`/`rest` (a fraction of the parent) after the P0 phone pass found 16px text
drawing at roughly a third size on a real phone. The fix that shipped
first (RUST.md's P0 box) was a global stopgap: divide the whole window
into a "logical" coordinate space (physical ÷ `content_scale`) and let
the shader's NDC mapping stretch it back up onto the real framebuffer.
That fixed the *size* but not the *sharpness* — a glyph rasterised at the
small, pre-stretch size and then stretched onto more physical pixels than
it has texels for is blurry, which is exactly what Iris's next report
said.

**The fix**: `Len` gained a `dp` field, resolved against a `density: f32`
(physical pixels per dp) at the one place a `Len` becomes a `UiScalar`
(`Len::apply_rest`) — `abs + dp * density`. `density` lives on
`UiRenderState` (`set_density`/`density()`) and `Painter` (`density()`),
set once from `DisplayMetrics.density` in `android::view::new_peer`; the
desktop backend has no per-monitor density wired up yet and stays at
`1.0`. Every layout call site that used to call `.apply_rest()`/
`.to_uivec2()` now passes `painter.density()` (nine call sites — `Span`,
`Sized`, `MaxSize`, `Aligned`, `Scroll`, `LazySpan::place`, and
`UiRenderState::place` itself). This also meant the Android
boundary's global logical-space stopgap could come out entirely: window
size, touch coordinates and insets are physical pixels again, matching
`AndroidRenderer`'s own swapchain resolution, with `dp` doing the
per-length work the global divide used to do for everything at once.

**Text is the case that needed more than the `Len` plumbing.** A widget's
`font_size`/`line_height` are plain `f32`, not routed through `Len` at
all (there is no sensible `rel`/`rest` for a font size). `TextBuffer::
shape` now takes `density` directly and multiplies `font_size`/
`line_height` (and any span override) by it before handing them to
parley — so the size that reaches both the line-breaker and the
rasteriser (`TextData::place`, which reads back whatever `shape` set) is
the display's *physical* size, and the glyph atlas holds a bitmap at the
resolution it is actually shown at. `GlyphKey.size` already keys on the
resolved size, so a cache entry is naturally per-physical-size with no
further change. The callers with no `Painter` to read density from (cursor
movement and hit-testing through `TextHandle::layout`) read a second copy kept
directly on `TextData` (`TextData::density`) instead — an
accepted duplication rather than threading a `Painter` into every input
handler for one field, the same tradeoff `AndroidRenderer::content_scale`
already makes for the Diagnostics page.

Glyph masks are cached at four horizontal quarter-pixel phases. Their final
quad edges snap to physical pixels after retained move offsets are applied;
the CPU mask geometry uses the same calculation as the shader. In particular,
a fractional scroll offset therefore moves text and other primitives in whole
physical-pixel steps instead of resampling the atlas vertically with the
nearest sampler.

**What did not change**: `rel`/`rest` are unaffected (already
resolution-independent, a fraction of the parent). `Span::gap` and
`Padding`'s four sides moved from bare `f32` to `Len` so `dp(...)` works
on them the same as any other size; a bare number is still `abs`,
physical pixels, unchanged.

## Masks

A `Mask` references a rectangle primitive and its parent mask. Nested masks
multiply coverage. Plain `.masked()` creates an undrawn rectangle at the
widget's region; `.masked_by(shape)` draws the shape behind the content and
clips to its first primitive. Keeping the shape in one primitive prevents a
rounded background and its clip from drifting apart.

Masks are rect-only. Glyph masks would require a CPU-readable alpha plane for
hit-test agreement, and standalone image masks require a bind-group switch the
fragment stage cannot make. Rendering and hit-testing both traverse the full
mask chain and use the same rounded-rectangle coverage; `iris/tests/mask_sdf.rs`
checks the WGSL implementation against the CPU SDF.

## Frames, decided boxes and padding

Containers that only divide room are transparent to fractions. A child frame
is narrowed by a length its parent decided: a declared `px` or `rel` length,
or the resolved slot of a `leftover` child. A box a widget reports for itself
does not narrow its descendants' frame.

`Pad` is an outset: it forwards its frame less the padding, draws the child
inside that area, and reports the child's used size plus padding. A
`rel(1.0)` child inside padding inside a share is a fraction of the resolved
share less that padding. The mixed "outset pixels, inset fractions and
shares" interpretation is rejected.

The current experiment still redraws some widgets in boxes derived from their
own answers. That is the open protocol defect, not a design invariant. The
target in `docs/HANDOFF.md` evaluates container bodies only in boxes a parent
offered or decided; placing an answer reuses or translates its drawing rather
than running the body in an answer-derived box.

## Layout decisions and invariants (2026-09-15 to 2026-09-17)

Moved here from the handoff on 2026-09-18. These are settled unless a
subsection explicitly says it is pending.

### Fixed point

Decided with Bryan on 2026-09-15. Layout decides on a grid rather than in
floats.

- **`Fixed<SHIFT>` is an `i32` counting `1 / 2^SHIFT`.** Adding and
  subtracting are exact; `mul` drops to the step below (Bryan, 2026-09-16:
  truncation is preferable); `div`, `div_int` and `ratio` round to nearest;
  `to_scale` takes the nearest step. Two routes to one place that land on
  one number are the same place, so everything downstream compares for
  equality.
- **`Px` is `1/1024` px, `Rel` is `1/2^24` of a box, `Weight` is `1/65536`
  of a share.** `PX_SHIFT` and `REL_SHIFT` are the only statement of the
  first two; the shader's copy is prepended from them by
  `render::module_source`. `Px` was `1/64` first, where one rounding's
  residue was 0.016 px and enough to move a box. Range is +/-2.1M px and
  conversion to `f32` is exact to 16,384 px.
- A weight is not a fraction: a list divides its room by the total of its
  weights, and `Rel::ratio` turns two weights into a share on the finer
  grid.
- **Arithmetic wraps** (`4febabf`, Bryan: a coordinate past the range will
  not draw reasonably anyway, so wrap and break clearly). Saturating cost a
  twelfth of layout's instructions. `MIN` and `MAX` stand in for an
  unbounded end and are only ever compared against; `from_f32` is the one
  operation that clamps, and `Holds` keeps a saturating `narrow`.
- A pointer, a wheel notch, a shaped glyph advance and a window size arrive
  as floats and go on the grid where they arrive. `Vec2` is what the GPU
  and the platform speak; `PxVec2` is what layout decides in.
- **Do not widen the grid to chase a residue.** Every failure seen was one
  value reached by two expressions, sitting on a boundary defined by the
  same value coming back the other way. No precision shrinks a residue that
  is the whole distance.
- **A value that comes back as a box is rounded away from the measurement,
  not to the nearest step.** `Fixed::ceil_from_f32` exists for that and is
  the only rounding on the grid that is not to nearest. Rounding to nearest
  is right for a value being carried and wrong for a bound; a text reporting
  `ceil` of its longest line is what keeps the box it is handed back one its
  line fits in (`4bd8607`).
- **A structural decision may not be taken on a hair's breadth.** A
  boundary that decides which children exist (a span's leftover split) is
  derived through the inverse of the expression that draws, never by a
  second expression for the same length: `mul` floors while `div` rounds,
  so a boundary derived with a division guards a drawing made with a
  multiply (`53b00c6`).

### A box in pixels is one multiply from its parent's

A draw threads pixel lengths down: the box a parent gave a widget, then the
part of that box its own answer placed its drawing in. `Painter::px_size`
and `px_len` read that value, and a local redraw takes the same steps back
up the parent chain (`asked_px`). Neither chain has a coordinate frame in it,
so a region node cannot break either, and warm and cold reach every length
by the same expression.

- **`Holds::through` is the exact preimage of `px + floor(rel * box)`**:
  `floor(rel * B) >= lo - px` is `rel * B >= (lo - px) << REL` and
  `floor(rel * B) <= hi - px` is `rel * B < (hi - px + 1) << REL`, two
  `div_toward`s once the sign of `rel` has said which bound is which. The
  answer is an interval even for a single length, because a floor is not
  invertible. The range has to contain the box a drawing was made in (the
  `Holds` assertion in `draw_at`, debug only) and must not contain a box
  the drawing does not hold for (the oracle); being the preimage makes
  those one statement rather than a trade-off.
- **Symbolic regions are for the GPU, hit testing and remaps alone.**
  `Moves::resolve` is the only walk left and it is the vertex shader's.
  Nothing layout decides is composed back up the move chain.
- **`px` is not stored on `ActiveData`, deliberately.** A resize every
  widget's `Holds` admits redraws nothing, so a stored pixel length would
  be stale on every widget in the tree with nothing to say so. `asked_px`
  walks up only where a widget is already being redrawn; the mean chain is
  2.8 levels.
- **The window is not a move entry** (`5b78002`). A chain bottoms out in
  `MoveIdx::NONE`; the window is applied where a fraction becomes pixels,
  `to_px(output_size)` on the CPU and the uniform in the shader. A resize
  rewrites no retained entry and re-uploads nothing but the uniform; its
  cost is whatever `Holds` redraws.
- **A move that keeps a box's length is a translation, and exact.** A box
  that changed length re-expresses each part as a fraction of the new one,
  which rounds. `tests/cases/drift.rs` pins that the grid does not drift
  either way. A length given in pixels is that many pixels wherever it ends
  up (`Len::within` adds a part's own pixels rather than scaling them);
  equal shares come out one or two steps apart because positions, not
  lengths, are what gets rounded, so the row fills and no two children
  leave a seam.

### Retained-layout invariants

- `Holds` is the interval of box lengths for which a widget's drawing and
  reported size remain valid. Reading `Painter::px_len` or `px_size` narrows
  it; `Painter::holds` widens it. The contract is trusted rather than checked
  defensively on every use.
- A retained drawing is reusable only when its `Holds` contains the new box
  on both axes, its parent and region-node choice match, it is on the layer it
  was drawn on, and the widget is clean. A valid ordinary subtree moves by
  recursive remap; a region node moves by one entry. A container that draws a
  child to learn its size uses `Painter::child_layer_at`, the layer the child
  will actually occupy.
- An answer's validity and its final drawing's validity are independent. A
  parent may reuse an answer while redrawing the placed output. Translate the
  drawing contract back through its placement; do not intersect it into the
  answer contract.
- A fraction resolves once against its frame. A report returns raw and is
  composed only where a parent narrowed that frame. A part's own pixel length
  is added rather than scaled, so a pixel length remains that many pixels at
  every nesting depth.
- An asked-but-undrawn size dependency belongs to the widget that asked. Keep
  it recorded so a later child change reaches the parent that decided not to
  draw it. Dirty size dependencies settle deepest-first.
- A widget that creates a mask clips to and reports its box. Its own mask and
  its inherited mask are distinct retained state: the former says which mask
  a move rewrites, while a local redraw receives the latter.
- A span's leftover/no-leftover boundary is a strict structural decision, not
  a tolerance. Derive the boundary through the inverse of the expression that
  places children. A cap may not contain `leftover`, because feeding the
  span's own room division back into a cap admits multiple fixed points.
- Text shaping is retained separately from line breaking. A greedy break
  holds from its longest produced line through the width at which it was
  made, expressed with `Painter::holds`.
- A region node stores one whole `UiRegion` in its parent node's coordinates;
  `FULL` is the identity. Changing node ownership redraws the subtree once,
  and a removed node's move entry remains alive until every descendant has
  migrated.
- Alignment is one value per axis and defaults to the middle because neither
  edge is neutral without a direction. One widget has one length per axis; a
  second length requires a second widget through `.wrapper()`.

### What the fuzzers tolerate

Warm and cold pixel regions must compare exactly; there is no step
allowance. When a row's grid-step count is not divisible by the number of
children, individual share widths differ, but every rerun of that layout
must still agree exactly.

### Rendering the grid (pending)

`snap_floor` in `prelude.wgsl` adds half a layout step before flooring,
which absorbs float error and not a layout step, so a third of 900 px
(299.999 on the grid) lands at 299 on screen. Bryan approved on 2026-09-17
rounding to the nearest pixel in the shader together with round-to-nearest
in `Fixed::mul` on the CPU, as one change with one verification; neither has
landed. The reason for the CPU half: a `Rel` is off by at most `2^-25` of
its box, so with round-to-nearest every product whose true value is a whole
number of steps is exact for boxes under about 8,000 px, where truncation
leaves half of them one step short and layout then decides "does not fit"
on a container the user meant to fit exactly. Use the branchless
round-half-up form, `(a * b + (1 << (BY - 1))) >> BY`; re-derive
`Holds::through` for it; check with `nm` that `UiSpan::within` still
inlines.

## Measuring layout cost on this machine

- **Check the work counters before comparing two commits' times.**
  `tests/layout_diagnostics.rs` prints drawn widgets, widget draws and
  primitive writes; a comparison is only worth reading when they match.
  `random.rs`'s `Branch` picks a subtree by a measured pixel length, so the
  fixture's shape moves with the thing measured; `Edits::fixed_branches`
  pins it for timing and the oracle keeps measured branches on purpose. A
  3x once reported was that artifact.
- **`perf stat` in this VM returns garbage readings** for both
  `instructions:u` and `cycles:u`, roughly a quarter of the time, off by a
  factor of five to fifteen. Take medians of nine or more and report how
  many readings a filter kept. Instruction counts hold to 0.02% within a
  binary and move 0.5% across a rebuild, so build the baseline beside the
  thing measured and quote a delta.
- **What moves cycles is whether `UiSpan::within` inlines.** It is the
  hottest line in layout; `nm` shows it as a symbol when it does not.
  Shrinking its body until the inliner takes it won; `#[inline]` on the
  body it had lost 1.5% cycles. Shrink it, do not annotate it.
- `Holds::through` divides twice per call and accounts for essentially all
  of a run's `i64` divisions: 2.8% of a 500-frame `many`.
- Tried and rejected, with numbers: a float reciprocal for the remap
  division, +6% cycles; branchless `shift_round`, +6.7%; removing the
  per-child hash lookup in `remap_subtree`, 0.0%; short-circuiting
  `apply_scalar` where the fraction is nought or one, +17%. Short-circuits
  guarding a saturating multiply stopped paying once the multiply wrapped;
  re-price a short-circuit before keeping it. Rust does not contract
  `a + b * c`. Wrapping (`4febabf`) was -8.6% instructions; truncating
  (`08c9d5a`) costs a share a thousandth of a pixel of its row.
- Threading the pixel box down the draw (2026-09-17) was free on cold
  layout and 9-13% of instructions off the retained paths, measured against
  `5b78002` at seed 1, depth 8, medians of 21.