Record rel_base and the container API, and sweep LAYOUT.md

`frame` is gone from the layout vocabulary in `docs/LAYOUT.md` too, since
leaving the design document in the old words defeats the rename; the
rendered-frame sense of the word is untouched. The `local == UiRegion::FULL`
item is dropped from the handoff: that comment was #18's and is not on the
review branch.

docs/HANDOFF.md

@@ -6,11 +6,11 @@ in `docs/LAYOUT_LOG.md`.
 
 ## The Iris layout repair is submitted
 
-**Iris PR #19** (`layout/one-ask`) replaces closed #18. The tip is `5642f20`:
+**Iris PR #19** (`layout/one-ask`) replaces closed #18. The tip is `aeb60e5`:
 `add6774` fixes collapsed-share placement, retained mask ownership and a
 redraw-on-reparent defect, `84dad21` removes repeated work in the test
-harness, and `5642f20` is the naming sweep below. The core design remains
-sound; round-to-nearest is still unchanged.
+harness, and `5642f20` and `aeb60e5` are the vocabulary and API work below.
+The core design remains sound; round-to-nearest is still unchanged.
 
 Two checkouts share one Git storage. `/home/bob/repos/iris` is the active
 `layout/one-ask` worktree; `ai-app-2/iris` stays on `main` at the app's
@@ -20,24 +20,42 @@ Each round was checked with format, workspace clippy under `-D warnings`, the
 workspace tests with and without `layout-diagnostics`, the release fast
 oracle, and the three prescribed seed scans — 400 at depth 5, 1,000 at depth
 6, 2,000 at depth 4. The cold dump covers 34,488 boxes: the fixes moved 650 of
-them, all from the collapsed-share correction, and the naming sweep moved
-none.
+them, all from the collapsed-share correction, and nothing since has moved
+one.
 
-## The naming sweep is done
+## The vocabulary and the container API are settled
 
-`5642f20` finished the rename decided on 2026-09-17, which `frame`'s return as
-a length had left half-applied. The box a parent asks a widget in is the
-**region**, and where its drawing ends up is its **placement**:
+`5642f20` finished the rename decided on 2026-09-17, which `frame`'s return
+as a length had left half-applied, and `aeb60e5` finished the word `frame`
+itself. Three names, and only two of them are boxes:
 
-- `Painter::extent` → `region`, and its `extent_len()` → `region_len()`.
-- `ActiveData::{part, extent}` → `{region, placement}`, and with them
-  `DrawInfo::part` and `Placing::extent`.
-- `LayoutHolds::{extent, extent_len}` → `{region, region_len}`, and
-  `Counter::OutsideExtent` → `OutsideRegion`.
-- `placed_extent` → `placement`, `frame_and_extent` → `frame_and_region`,
-  `part_of` → `region_of`.
-- `Painter`'s `window_own`, `extent_own`, `frame_own_len` and `extent_len`
-  become the one `own: LayoutHolds` they were assembled into.
+- **region** -- the box a parent asks a widget in. It draws there, and a text
+  wraps at it. Was `Painter::extent`, `ActiveData::part`, `DrawInfo::part`,
+  `Placing::extent`, `LayoutHolds::extent`.
+- **placement** -- the box its drawing ends up in, the size it reported,
+  once it has answered. Equal to the region wherever it fills one. Was
+  `ActiveData::extent`; `placed_extent` is now `placement`.
+- **rel_base** -- not a box: the length a fraction it declares or reports is
+  a fraction of. Was `frame`, which said the wrong shape.
+  `Painter::frame_len()` is `Painter::rel_base()`, `LayoutHolds::frame_len`
+  is `rel_base`, and `frame_and_extent` is `rel_base_and_region`.
+
+`aeb60e5` also cut what a container has to say, since correctness and cost
+had been paid for and ergonomics had not:
+
+- `Painter::widget_within(id, region)` takes a box in the widget's own
+  coordinates and derives the child's rel base from it, so `Pad` and
+  `Offset` are one call each. `Offset` had been reading `region_len`, which
+  pinned its drawing to a box length an offset does not depend on.
+- `Painter::place_at` takes the rel base, returns the answer, and draws the
+  child where there is no answer to re-express. `Span`'s second pass is one
+  call, and its `drawn_across` bookkeeping is gone.
+- `Part::All` is a `Part::WHOLE` constant rather than a variant. It was
+  exactly `Of(UiSpan::FULL)`; measured at 0.07% of instructions retired
+  against 0.04% run-to-run noise on a 60-seed depth-5 shrink.
+
+Cold layout is byte-identical to `84dad21` across all of it, over 400
+depth-5 trees.
 
 ## What is next, in order
 
@@ -50,9 +68,10 @@ a length had left half-applied. The box a parent asks a widget in is the
    `32f6ad8` has 45 commits not reachable from the review branch; shared UI
    ownership, richer masks, Android support, and app-side performance work
    must survive the integration. The app then absorbs the branch's
-   vocabulary, all of it already upstream: `rest` → `leftover`, `SizeRule`
-   beside widgets, alignment properties, the removal of `OrthoSize`, and the
-   region/placement names above.
+   vocabulary and container API, all of it already upstream: `rest` →
+   `leftover`, `SizeRule` beside widgets, alignment properties, the removal
+   of `OrthoSize`, the region/placement/rel_base names above, and
+   `widget_within`/`place_at`.
 3. **Round-to-nearest**, CPU and shader together as one verified change.
    Bryan approved it on 2026-09-17 and neither half has landed; the
    derivation, the form to use and what to re-check are in `docs/LAYOUT.md`
@@ -67,9 +86,6 @@ a length had left half-applied. The box a parent asks a widget in is the
   children and nothing states what a widget may assume about one.
 - `Fixed::div` by zero answers `MIN`/`MAX` while `ratio` answers `ZERO`; both
   are caller bugs under `debug_assert`, but the fallbacks differ.
-- The comment on the `local == UiRegion::FULL` shortcut in `widget_at` says
-  composing through `FULL` "is not quite the identity in f32"; on the grid it
-  is exact and the shortcut is performance only.
 - `docs/LAYOUT.md` §4, §5 and the density section name `Painter::place`,
   `Painter::region()`, `SetSize`, `desired_width`, `apply_rest`, `Len::dp`,
   `Aligned` and `MaxSize`, none of which exist. Do not restore

docs/LAYOUT.md

@@ -8,7 +8,7 @@ without reading that result does not make the parent's size depend on it.
 carries those commits whole plus the retained-layout repair built on them. §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 where the work
-in flight stands. The sections from "Frames, decided boxes and padding"
+in flight stands. The sections from "Rel bases, decided boxes and padding"
 onwards are the settled design, the findings that outlived the working log,
 and the measurement method.
 
@@ -302,7 +302,7 @@ physical pixels, unchanged.
 
 ## Masks
 
-This section and "UI ownership and frame access" describe the app's pinned
+This section and "UI ownership and rel base access" describe the app's pinned
 Iris implementation. The upstream #19 review branch still has single
 rectangular masks and separate `UiData`/`UiRenderState`; adopting it requires
 integrating the app-side capabilities as well as migrating layout calls.
@@ -319,18 +319,18 @@ 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
+## Rel bases, decided boxes and padding
 
-Containers that only divide room are transparent to fractions. A child frame
+Containers that only divide room are transparent to fractions. A child rel base
 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.
+does not narrow its descendants' rel base.
 
 `Pad` is an inset (Bryan, 2026-09-18): it subtracts the padding from both
-the child's frame and the child's box, and reports the child's size plus the
+the child's rel base and the child's box, and reports the child's size plus the
 padding. A `rel(1.0)` child inside padding fills the pad without overflowing
 it; a wrapping text inside padding wraps at the box the pad was given less
-the padding. A span's frame never subtracts siblings, so a padded fixed
+the padding. A span's rel base never subtracts siblings, so a padded fixed
 child measured after a 24 px sibling in a 900 px row wraps at 844 while a
 `rel(1.0)` inside it is 868. There is no outset kind and no mixed kind.
 
@@ -349,13 +349,13 @@ asserted exactly that and was unsatisfiable.
 A container that can learn a child's length without drawing it does.
 `Painter::size_hint` answers from the child's rule, or from
 `Widget::size_hint` where it implements one, resolved against the asking
-widget's frame; `Scroll`, `Masked` and a `Stack` without a sizing child hint
+widget's rel base; `Scroll`, `Masked` and a `Stack` without a sizing child hint
 `LEFTOVER`, since each always reports the whole of its box. `Span` takes each
 child's length from its hint where there is one and asks that child exactly
 once, in the slot it decided; a child with no hint is drawn in the room left
 from the cursor, because a text has to wrap at the width actually there, and
 its drawing is moved to its slot with `place_at`. Reading a hint records a
-size dependency and pins the frame where the hint declared a fraction, the
+size dependency and pins the rel base where the hint declared a fraction, the
 same pin a rule that is a fraction takes.
 
 **What that leaves, and the design that would remove it.** A widget that
@@ -373,23 +373,23 @@ either answer moved, which also retires `re_asked`'s deferral. Do it only
 once an app screen shows the cost, and measure that screen first.
 
 **There is one coordinate unit, the window** (`1512d84`, `23523ee`). Every box in the
-tree is a region in window units; a widget's frame is a *length* in the same
+tree is a region in window units; a widget's rel base is a *length* in the same
 units and is only what fractions resolve against, so a widget's box need not
-be its frame and padding can take from both. A region node's entry is a
+be its rel base and padding can take from both. A region node's entry is a
 translation -- a `rel 1` region anchored where its box starts -- so nothing
-composes a frame back up a chain.
+composes a rel base back up a chain.
 
-A frame decided for a child is therefore a length of the window too: a row's
-slot, padding's frame less its pixels, or the box a stack's sizing child
+A rel base decided for a child is therefore a length of the window too: a row's
+slot, padding's rel base less its pixels, or the box a stack's sizing child
 decided (which arrives as `Part::Sized`). It is never a fraction of the
-parent's frame, because a slot of a row is not a fraction of anything the row
+parent's rel base, because a slot of a row is not a fraction of anything the row
 can name -- a division of two lengths, which a `rel + px` length cannot hold.
 A widget's own declaration *is* a fraction, of whichever of those reached it,
 and it is the only one of them that also places the box inside the part.
 
 Validity has a pin for each: `LayoutHolds::region_len` for the box's symbolic
-length and `frame_len` for the frame's. A range of window pixels cannot say
-which frame an answer is a fraction of, since two frames are different
+length and `rel_base` for the rel base's. A range of window pixels cannot say
+which rel base an answer is a fraction of, since two rel bases are different
 lengths at the same window size. Resolving any of these lengths in pixels is
 a read of the window, and `Painter::to_px` is where that read is taken --
 pinning the window where the length has a fraction in it, and nothing where
@@ -449,10 +449,10 @@ floats.
 
 Every length in the tree is a length of the window, so it becomes pixels in
 one multiply wherever it is read: `Painter::px_size` and `px_len` for the
-box, `frame_len` for the frame. There is no chain to walk and no coordinate
-frame in the way, so a region node cannot break it and warm and cold reach
-every length by the same expression. (Before `1512d84` a frame was a length
-of its parent's frame and a local redraw walked back up the parent chain in
+box, `rel_base` for the rel base. There is no chain to walk and no coordinate
+rel base in the way, so a region node cannot break it and warm and cold reach
+every length by the same expression. (Before `1512d84` a rel base was a length
+of its parent's rel base and a local redraw walked back up the parent chain in
 `asked_px`; both are gone.)
 
 - **`Holds::through` is the exact preimage of `px + floor(rel * box)`**:
@@ -470,7 +470,7 @@ of its parent's frame and a local redraw walked back up the parent chain in
 - **`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. What is
-  stored is the symbolic frame, which a redraw resolves against the window
+  stored is the symbolic rel base, which a redraw resolves against the window
   it has.
 - **The window is not a move entry** (`5b78002`). A chain bottoms out in
   `MoveIdx::NONE`; the window is applied where a fraction becomes pixels,
@@ -502,8 +502,8 @@ of its parent's frame and a local redraw walked back up the parent chain in
   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
+- A fraction resolves once against its rel base. A report returns raw and is
+  composed only where a parent narrowed that rel base. 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
@@ -557,7 +557,7 @@ must still agree exactly.
   parts from cold at every other window. There is still no case that changes
   a tree twice with a resize between, and none that resizes twice.
 - The fuzzer grows no `rel` rules and never re-parents a widget, so neither
-  a fraction resolved against a frame nor a subtree changing hands is
+  a fraction resolved against a rel base nor a subtree changing hands is
   covered by any generated tree. Both have cost a defect that only a
   hand-written expectation or a render caught.
 
@@ -568,8 +568,8 @@ must still agree exactly.
   existed only because a widget was drawn twice; one draw leaves it nothing
   to name. A plan that proposes bookkeeping for a distinction should first
   ask whether the distinction has to exist.
-- **A frame narrowed by a region does not move when its part moves.** A
-  narrowed frame must be a *length*, put back into the part on every
+- **A rel base narrowed by a region does not move when its part moves.** A
+  narrowed rel base must be a *length*, put back into the part on every
   placement, exactly as a declared rule already is.
 - **Choosing between a fixed and a relative child in pixels at the span's
   current width** admits multiple self-sizing fixed points; seed 13 settles
@@ -584,8 +584,8 @@ must still agree exactly.
   phase. A symbolic pin survives a resize because every ask box is
   symbolically stable across one, so the pin only fails where an answer
   changed, which is a real relayout.
-- **Resolving a rule that is a fraction of the frame from the record instead
-  of redrawing** recovers nothing: `reuse outside: a frame length` is 3 of
+- **Resolving a rule that is a fraction of the rel base from the record instead
+  of redrawing** recovers nothing: `reuse outside: a rel base` is 3 of
   264 cold draws at seed 1 and 1 of 758 at seed 13.
 - **A `git bisect`** once named a commit that could not be the cause; read
   the tree rather than the bisect when that happens.

docs/LAYOUT_LOG.md

@@ -138,7 +138,7 @@ The descriptions above preserve the original failure at `cadfba0`.
 
 The first three -- the unswept `extent`, the two same-typed boxes on
 `ActiveData`, and `Painter`'s four holds accumulators -- were done in
-`5642f20`. What is left:
+`5642f20`, and `Part::All` in `aeb60e5`. What is left:
 
 - `draw_inner` returns `(Size, LayoutHolds, LayoutHolds)`, two same-typed
   values ordered by convention. A named pair makes the swap unwriteable.
@@ -152,9 +152,3 @@ The first three -- the unswept `extent`, the two same-typed boxes on
   `under.iter_mut().find`, `depend_on`), so a span of *n* children is
   O(n^2) per draw. Not a problem at today's sizes; it is worth knowing
   before a long transcript list lands on it.
-- `Part::All` is exactly `Part::Of(UiSpan::FULL)`: `Of` composes through
-  `within`, and `through(Len::FULL)` maps a range back to itself, which
-  `the_whole_of_a_box_maps_back_to_itself` already asserts. It buys a
-  separate arm in `in_parent` and in `Part::of`. Keeping it as sugar is
-  defensible; the case analysis being wider than the geometry is the thing
-  to decide about rather than to leave unstated.