docs(P1): align wording with level-list API only

Drop legacy constructor prose (child=/mutual exclusion), retarget
README and fixed_three_level_multipatch examples to refinements /
level_blocks, and fix stepper error/doc strings that still named
fine_block/base_block or a fixed gap >= 4 (unions use dependency
closure). Wording only; no behavior change.

README.md

@@ -125,8 +125,8 @@ with CudaContext(0) as ctx, FixedPatchStepper(cfg, context=ctx, refinements=[(8,
 
 Scope and limits:
 - The examples below use D2Q9, SRT, FP32, double buffer, unshifted, no LES or
-  forcing. Fixed 2:1 hierarchies can use level lists of arbitrary depth; the
-  legacy two/three-level forms are shown below.
+  forcing. Fixed 2:1 hierarchies use level lists of arbitrary depth; two- and
+  three-level examples below use that same constructor.
 - `coarse_boundary="periodic"` (default) or `"slot_reservoir"` (bottom slot, top
   reservoir; patch needs `y0 >= 4`, `y1 <= ny-4`). Periodic mode ignores the wall/slot config fields.
 - Object centers/radii use the coarse **cell-edge** frame (cell `I` spans `[I, I+1)`),
@@ -151,7 +151,7 @@ Scope and limits:
   inside the union's active region with
   its boundary stencil clear of transfer cells; a jet may not select links of two
   different bodies, even across regions. Wall-touching patches remain unsupported.
-  For nesting, use the level lists or legacy child forms below.
+  For nesting, add further `refinements` entries as shown below.
 
   ```python
   cfg = LBMConfig(nx=32, ny=16, viscosity=.1)
@@ -165,19 +165,20 @@ Scope and limits:
       coarse_g, fine_g = run.download()  # coarse: NaN on every covered cell;
                                          # fine: NaN on every non-ACTIVE cell
   ```
-- Legacy three-level scalar chain: add `child=(x0, y0, x1, y1)` in
-  **L1 window cells** (the patch's fine grid including its 4-cell ghost band) and
-  all three `level_blocks` entries. L2 must sit inside L1's
-  ACTIVE cells, away from L1's ghost band and transfer footprint (checked before
-  any GPU allocation). `initialize` and `download` take/return three arrays; each
-  level is NaN on its non-ACTIVE (and child-covered) cells. One coarse step = 2 L1
-  steps = 4 L2 steps. One L1 patch only. Optional stationary circles and Jets
-  live on L2 via `level_objects[2]` and `level_jets[2]`; L1 bodies/Jets retain
-  their L1 meaning and must be empty in this mode. All object and Jet geometry
-  uses the **L0 edge frame**, not the child bounds' L1 window frame. L2 has
-  dx=dt=0.25, so prescribed lattice velocity is unchanged. Each whole body and
-  its BFL stencil must be inside L2 ACTIVE cells, outside the transfer footprint.
-  A Jet may select one physical body across multiple blocks, never two bodies.
+- Three-level nested windows: pass two scalar rectangles in `refinements` —
+  L1 in L0 cells, L2 in **L1 window cells** (the parent's fine grid including its
+  4-cell ghost band) — plus all three `level_blocks` entries. L2 must sit inside
+  L1's ACTIVE cells, away from L1's ghost band and transfer footprint (checked
+  before any GPU allocation). `initialize` and `download` take/return three
+  arrays; each level is NaN on its non-ACTIVE (and child-covered) cells. One
+  coarse step = 2 L1 steps = 4 L2 steps. One L1 window only in this scalar
+  chain. Optional stationary circles and Jets live on L2 via `level_objects[2]`
+  and `level_jets[2]`; L1 bodies/Jets retain their L1 meaning and must be empty
+  in this mode. All object and Jet geometry uses the **L0 edge frame**, not the
+  child bounds' L1 window frame. L2 has dx=dt=0.25, so prescribed lattice
+  velocity is unchanged. Each whole body and its BFL stencil must be inside L2
+  ACTIVE cells, outside the transfer footprint. A Jet may select one physical
+  body across multiple blocks, never two bodies.
 
   ```python
   from CelerisLab.body.geometry.circle import CircleGeometry
@@ -199,16 +200,16 @@ Scope and limits:
       run.step(4)
       coarse_g, l1_g, l2_g = run.download()  # solids/covered/nonleaves are NaN
   ```
-- Level lists: `refinements[l]` describes level `l+1` in allocated level-`l`
-  integer cells; use a rectangle list for a union, or a scalar rectangle for a
-  single window (a scalar child requires a scalar parent). `level_blocks`,
-  `level_objects` and `level_jets` each have one entry per level, including L0.
-  These lists are mutually exclusive with the legacy patch keywords. Three or
-  more levels require all-blocked storage and bodies/Jets only on the finest
-  level. Every adjacent pair must preserve inherited ACTIVE coverage, valid
-  donors/receivers, surviving pulls and the upstream transfer footprint.
-  Level `l` takes `2**l` steps per base interval. This describes implemented
-  topology and scheduling, not accuracy or convergence qualification.
+- Level lists (the only constructor): `refinements[l]` describes level `l+1`
+  in allocated level-`l` integer cells; use a rectangle list for a union, or a
+  scalar rectangle for a single window (a scalar child requires a scalar
+  parent). `level_blocks`, `level_objects` and `level_jets` each have one entry
+  per level, including L0. Three or more levels require all-blocked storage and
+  bodies/Jets only on the finest level. Every adjacent pair must preserve
+  inherited ACTIVE coverage, valid donors/receivers, surviving pulls and the
+  upstream transfer footprint. Level `l` takes `2**l` steps per base interval.
+  This describes implemented topology and scheduling, not accuracy or
+  convergence qualification.
 - Blocked body levels can enable `observe_raw_exchange=True` and call
   `read_raw_exchange(body_id, level=...)` after a completed base interval.
   It reduces unique cut-link observations into wall/aperture/total force,

docs/fixed_three_level_multipatch.md

@@ -1,8 +1,8 @@
 # Fixed three-level rectangle unions
 
-This page describes the legacy three-level entry point of `FixedPatchStepper`,
-with rectangle unions on either adjacent pair. The `refinements` level-list
-entry point also supports arbitrary depth; three or more levels require
+This page describes three-level `FixedPatchStepper` setups built from the
+`refinements` level list, with rectangle unions on either adjacent pair. The
+same constructor supports arbitrary depth; three or more levels require
 all-blocked storage and bodies/Jets only on the finest level. This is not
 general AMR: there is no per-region timestep, moving geometry, automatic
 dynamic refinement or L1 body support in the three-level form.
@@ -12,15 +12,15 @@ No CUDA kernel changes are involved.
 
 ## Explicit coordinate frames
 
-Keep the existing scalar `child=(x0,y0,x1,y1)` for a single scalar parent patch.
-Its coordinates retain their original meaning: half-open integer indices in the
-allocated L1 window, including its ghost band.
+For a single scalar parent patch, pass a scalar rectangle as `refinements[1]`:
+`(x0,y0,x1,y1)` in half-open integer indices of the allocated L1 window,
+including its ghost band.
 
-A rectangle list as the second `refinements` entry (formerly the keyword
-`child_rectangles_in_parent=[...]`) accepts a scalar or a set parent and interprets every rectangle in
-the actual allocated L1 array, including ghost bands and holes. It never infers
-region-local coordinates. The physical root cell edge corresponding to an L1
-index `(x,y)` is `parent.fine_origin + (x,y)/2`:
+A rectangle list as `refinements[1]` accepts a scalar or a set parent and
+interprets every rectangle in the actual allocated L1 array, including ghost
+bands and holes. It never infers region-local coordinates. The physical root
+cell edge corresponding to an L1 index `(x,y)` is
+`parent.fine_origin + (x,y)/2`:
 
 - A scalar L1 parent has a shifted window origin.
 - A set L1 parent has origin `(0,0)` and public shape `(2*ny,2*nx)`.

src/CelerisLab/lbm/refinement_stepper.py

@@ -75,13 +75,13 @@ def _check_levels(refinements, blocks, objects, jets):
             raise ValueError(f"{name} needs one entry per level ({depth})")
     for level, block in enumerate(blocks):
         if block is not None and len(block) != 2:
-            raise ValueError(f"{_level_name(level)}_block must be (by, bx)")
+            raise ValueError(f"level_blocks[{level}] must be (by, bx)")
     if objects[0] or jets[0]:
         raise ValueError("base-level bodies/Jets are not supported")
     if any(blocks[level - 1] is not None and blocks[level] is None for level in range(1, depth)):
         raise ValueError("a blocked level requires blocked refined levels below it")
     if not is_rectangle(refinements[0]) and (blocks[0] is None or blocks[1] is None):
-        raise ValueError("several patches require fine_block and base_block")
+        raise ValueError("several L1 patches require level_blocks[0] and level_blocks[1]")
     if depth > 2:
         if any(block is None for block in blocks):
             raise ValueError("three or more levels must all be blocked")
@@ -149,9 +149,11 @@ class FixedPatchStepper:
     Nested levels: a child set's coordinates index the allocated parent array,
     including ghost bands and holes: root edge = parent fine_origin + index / 2
     (zero origin for a parent set; a scalar parent keeps its shifted window
-    origin). A scalar child requires a scalar parent. Each pair requires gap >= 4
-    in its own parent-cell units. All regions share one buffer pair per level
-    and the fixed schedule of 2**l hops per base step at level l. Bodies/Jets are supported only on the
+    origin). A scalar child requires a scalar parent. Rectangle unions impose no
+    fixed gap rule: adjacent, overlapping and concave unions are accepted when
+    their actual transfer dependencies close (FixedPatchSet2D /
+    nest_patch_set). All regions share one buffer pair per level and the fixed
+    schedule of 2**l hops per base step at level l. Bodies/Jets are supported only on the
     finest level of a nested hierarchy (L2 dx=dt=.25 in root units, unchanged
     lattice velocity); every whole circle and its BFL stencil must fit strictly
     away from that level's transfer footprint.