fix: seat the ladder rungs and stop the iron chamfers reading as wood

docs/gallery/index.html

@@ -1151,12 +1151,12 @@ <h2><a href="iron-cauldron/">iron-cauldron</a></h2>
       </article>
       <article class="card" data-tags="mesh export showcase">
         <a class="card-media" href="wooden-ladder/" aria-label="wooden-ladder example detail page">
-          <img src="assets/wooden-ladder-hero.webp" alt="wooden-ladder — A procedural timber ladder with raked stiles, six rungs, and iron shoes through UVs, bake, LOD, collider, and Unity glTF, asserting recomputed budgets rather…" loading="lazy" decoding="async" />
+          <img src="assets/wooden-ladder-hero.webp" alt="wooden-ladder — A procedural timber ladder with raked stiles, six dowel rungs tenoned into the stiles, and iron shoes and top caps through UVs, bake, LOD, collider, and Unity…" loading="lazy" decoding="async" />
         </a>
         <div class="card-body">
           <h2><a href="wooden-ladder/">wooden-ladder</a></h2>
-          <p class="teaches">A procedural timber ladder with raked stiles, six rungs, and iron shoes through UVs, bake, LOD, collider, and Unity glTF, asserting recomputed budgets rather than an API contract.</p>
-          <p class="witnesses"><span class="tag">witnesses</span> Recomputed: 2184 tris, two materials with 1008 wood and 48 metal faces, UVs in 0..1 with zero AABB overlap, outer AABB 0.474×0.361×1.482 m, LOD ratios in band, convex collider 52 tris, non-empty glTF. --skip-decimate exits 9 on the LOD1 ratio budget.</p>
+          <p class="teaches">A procedural timber ladder with raked stiles, six dowel rungs tenoned into the stiles, and iron shoes and top caps through UVs, bake, LOD, collider, and Unity glTF, asserting recomputed budgets rather than an API contract.</p>
+          <p class="witnesses"><span class="tag">witnesses</span> Recomputed: 936 tris, two materials with 324 wood and 216 metal faces, UVs in 0..1 with zero AABB overlap, outer AABB 0.472×0.365×1.460 m, grounded at zmin 0, mesh hygiene all zero, 12 shells with every rung clearing the stile chamfer by 3.61 mm, convex collider 24 tris, non-empty glTF. Four falsifiers exit 9, 15, 16, and 17 on the LOD, hygiene, grounded, and joint-fit budgets.</p>
           <a class="card-link" href="wooden-ladder/">View example <span aria-hidden="true">&rarr;</span></a>
         </div>
       </article>

showcase/README.md

@@ -34,7 +34,11 @@ entry in `showcase/gallery.json`, and a rendered still.
 - **Falsifier** breaks one pipeline stage so a **named** budget fails and
   the piece exits its documented code. Prove default and falsifier on
   4.5.11, 5.1.2, and 5.2.1. `--skip-decimate` is the LOD-ratio
-  falsifier (exit 9). `--lift-z` is the grounded-zmin falsifier (exit 16).
+  falsifier (exit 9), `--stray-vert` the mesh-hygiene falsifier (exit
+  15), `--lift-z` the grounded-zmin falsifier (exit 16), and
+  `--fat-rungs` (or the piece's equivalent) the joint-fit falsifier
+  (exit 17). A budget with no falsifier witnesses nothing: prove each
+  one fails once, and check the exit code, not just non-zero.
 - **Hygiene budgets.** Copied combinatorics from
   `examples/mesh-hygiene-audit` (do not import the example). Every piece
   asserts on the generated mesh: non-manifold edges 0, loose verts 0,
@@ -43,6 +47,17 @@ entry in `showcase/gallery.json`, and a rendered still.
   characteristic 2 — that is a single-shell contract. Pairs of parts
   meant to touch assert a BVH surface gap below a named epsilon
   (vert-vert is the wrong metric for thin straps and collars).
+- **Joint-fit budgets.** Parts that interpenetrate on purpose — a tenon
+  in a mortise, a peg in a hub — assert how deep the overlap goes, not
+  just that it exists. Split the mesh into shells by edge connectivity,
+  assert the expected shell count, and for each joint assert three
+  named minima recomputed from vertex positions: the inserted part stays
+  clear of the host's chamfer, it seats far enough past the host's near
+  face, and it stops short of the host's far face. A part exactly as
+  thick as its host passes a "parts overlap" test while erupting through
+  the host's chamfer as a spike — that is the class this catches.
+  Measure in the construction frame (un-rotate by any rake) so a tilted
+  host does not inflate its own AABB.
 - **Material face floors.** Every declared material asserts a named
   minimum face count on the finished mesh, recomputed from
   `polygon.material_index`. This catches the slot-assignment wipe class:

showcase/gallery.json

@@ -296,8 +296,8 @@
     {
       "name": "wooden-ladder",
       "dir": "showcase/wooden-ladder",
-      "teaches": "A procedural timber ladder with raked stiles, six rungs, and iron shoes through UVs, bake, LOD, collider, and Unity glTF, asserting recomputed budgets rather than an API contract.",
-      "witnessesFix": "Recomputed: 2184 tris, two materials with 1008 wood and 48 metal faces, UVs in 0..1 with zero AABB overlap, outer AABB 0.474×0.361×1.482 m, LOD ratios in band, convex collider 52 tris, non-empty glTF. --skip-decimate exits 9 on the LOD1 ratio budget.",
+      "teaches": "A procedural timber ladder with raked stiles, six dowel rungs tenoned into the stiles, and iron shoes and top caps through UVs, bake, LOD, collider, and Unity glTF, asserting recomputed budgets rather than an API contract.",
+      "witnessesFix": "Recomputed: 936 tris, two materials with 324 wood and 216 metal faces, UVs in 0..1 with zero AABB overlap, outer AABB 0.472×0.365×1.460 m, grounded at zmin 0, mesh hygiene all zero, 12 shells with every rung clearing the stile chamfer by 3.61 mm, convex collider 24 tris, non-empty glTF. Four falsifiers exit 9, 15, 16, and 17 on the LOD, hygiene, grounded, and joint-fit budgets.",
       "hero": "docs/gallery/assets/wooden-ladder-hero.webp",
       "preview": "showcase/wooden-ladder/preview.webp",
       "tags": [

showcase/wooden-ladder/README.md

@@ -1,9 +1,9 @@
 # Wooden ladder
 
 A showcase piece, not an example. Procedural timber ladder (raked
-stiles, six rungs, iron shoes and straps) then the shipped pipeline:
-unique-cell UVs, Cycles high-to-low normal bake, LOD chain, convex
-collider, Unity glTF export.
+stiles, six 26 mm dowel rungs tenoned into the stiles, iron shoes and
+top caps) then the shipped pipeline: unique-cell UVs, Cycles
+high-to-low normal bake, LOD chain, convex collider, Unity glTF export.
 
 It asserts **budget conformance** of the generated result. It does not
 witness an API contract. "It rendered without error" is not a check.
@@ -21,14 +21,34 @@ materials, UVs, evaluated LOD, collider, or export file.
 
 | Axis | Declared | Measured (4.5.11 / 5.1.2 / 5.2.1) |
 | --- | --- | --- |
-| Base triangles | 2100–2280 | 2184 / 2184 / 2184 |
+| Base triangles | 900–975 | 936 / 936 / 936 |
 | LOD1 ratio | 0.32–0.62 of base | 0.5000 / 0.5000 / 0.5000 |
-| LOD2 ratio | 0.10–0.35 of base | 0.2198 / 0.2198 / 0.2198 |
-| Materials | exactly 2 distinct, ≥24 wood, ≥24 metal | 2 slots, 1008 wood, 48 metal |
+| LOD2 ratio | 0.10–0.35 of base | 0.2179 / 0.2179 / 0.2179 |
+| Materials | exactly 2 distinct, ≥280 wood, ≥180 metal | 2 slots, 324 wood, 216 metal |
 | UVs | in `0..1`, AABB overlap ≤ 1e-5 | in range, overlap 0 |
-| Outer AABB | (0.474, 0.361, 1.482) m ± 0.01 | (0.4740, 0.3612, 1.4823), zmin 0 |
-| Collider tris | ≤ 120 | 52 |
-| Export | written, size > 0 | 158256 / 158256 / 158240 bytes |
+| Outer AABB | (0.472, 0.365, 1.460) m ± 0.01 | (0.4720, 0.3649, 1.4597) |
+| Grounded | `abs(zmin)` ≤ 1e-4 | 0.0000 |
+| Mesh hygiene | non-manifold, loose v/e, doubles at 1e-5, zero-area, n-gons all 0 | all 0 |
+| Parts | exactly 12 shells (2 stiles, 6 rungs, 2 caps, 2 shoes) | 12 (2 / 6) |
+| Rung depth clearance | ≥ 0.003 m inside the stile faces | 0.00361 |
+| Tenon engagement | ≥ 0.006 m past the stile inner face | 0.01200 |
+| Tenon breakout margin | ≥ 0.005 m short of the stile outer face | 0.04600 |
+| Collider tris | ≤ 120 | 24 |
+| Export | written, size > 0 | 75140 / 75140 / 75128 bytes |
+
+Base triangles fell from **2184 to 936** in the quality pass: four iron
+fittings per stile collapsed to one shoe and one top cap, and the
+redundant top block came out. No hidden-face removal was involved.
+
+The rung rims are capped and buried in the stile rather than left open.
+That costs 144 tris nobody sees, but an open rim is a non-manifold
+boundary and the hygiene budget forbids it.
+
+The joint budgets are measured per rung against each stile, from vertex
+positions in the un-raked construction frame, and the reported value is
+the worst case over all twelve rung ends. `clearance` is how far the
+widest dowel stays inside the stile's front and back faces; it must
+exceed the 2.5 mm chamfer or the dowel erupts through it as a spike.
 
 DECIMATE COLLAPSE triangle counts are **not** identical across series —
 the gate is a ratio band, not an exact count. On this mesh the three
@@ -37,18 +57,31 @@ binaries agreed on LOD ratios. Bake pixels are stochastic; the gate is
 uses no RNG. Export byte counts differ by 16 B on 5.2.1 (glTF
 serializer), not a gated axis.
 
-`--skip-decimate` skips the LOD DECIMATE stage so LOD1 ratio is 1.0 and
-exit 9 fires. That is the named budget the falsifier violates.
+Each falsifier violates exactly one named budget, and each was proven to
+fire on all three binaries:
+
+| Falsifier | Budget violated | Exit | Measured failure |
+| --- | --- | --- | --- |
+| `--skip-decimate` | LOD1 ratio band | 9 | ratio 1.0000 |
+| `--stray-vert` | Mesh hygiene, loose verts | 15 | `loose_v=1` |
+| `--lift-z` | Grounded zmin | 16 | zmin 0.050000 |
+| `--fat-rungs` | Rung depth clearance | 17 | clearance −0.00051 |
+
+`--fat-rungs` widens the dowels to the full 34 mm stile depth, which is
+the proportion this piece shipped with before the quality pass.
 
 ## Run
 
 ```bash
 blender --background --python wooden_ladder.py --
 blender --background --python wooden_ladder.py -- --skip-decimate
+blender --background --python wooden_ladder.py -- --stray-vert
+blender --background --python wooden_ladder.py -- --lift-z
+blender --background --python wooden_ladder.py -- --fat-rungs
 blender --background --python wooden_ladder.py -- --output ladder.png
 ```
 
-Smoke does not pass `--output` or `--skip-decimate`.
+Smoke passes no flags: no `--output`, no falsifier.
 
 ## Exit codes
 
@@ -72,3 +105,6 @@ File-local. `9` is a valid check code. `10` is reserved for
 | 12 | Bake did not finish or image has no data |
 | 13 | Export file missing or empty |
 | 14 | `--output` produced no file |
+| 15 | Mesh hygiene (`--stray-vert` lands here) |
+| 16 | World AABB min Z off the floor (`--lift-z` lands here) |
+| 17 | Part count or rung-to-stile joint fit (`--fat-rungs` lands here) |