fix(examples): redesign armature-bend as ribbed bellows hoses on steel flanges

The tube is now lathed from an (r, z) profile: brass collars at both ends
and a ribbed rubber bellows between, standing on render-only steel foot
flanges with brass bolt heads. Every weight is still a function of z alone,
so the closed-form LBS check is untouched; the ribs make the bend legible
(open on the outside of the curl, crowded on the inside). BoneTint colours
the rib crests, and a Crest attribute darkens the valleys. The render path
now runs the gallery_framing gate (exit 10), which it previously skipped.

Evidence (live runs, local):
- .scratch/blender-5.2.1-windows-x64/blender.exe (Blender 5.2.1 LTS):
  check-only exit 0, bones=4 verts=6688 lbs_max_err=5.33e-07
  tip_deflection=3.188. --zero-curl exits 8 ("tip only moved 0.0000").
- .scratch/blender-4.5.11-windows-x64/blender.exe (Blender 4.5.11 LTS):
  check-only exit 0, same numbers.
- Framing: fill x=0.688 y=0.789, margins l=0.106 r=0.137 b=0.100 t=0.067.
- Contact sheet (docs/gallery/contact-sheets/armature-bend-contact-sheet.webp):
  candidate luma 0.243 / stage 0.192 / warmth -0.144 / sat 0.237, against
  damped-track-aim 0.151/0.145/+0.277/0.231 and bmesh-gear 0.236/0.177/+0.303/0.250.
  Saturation and stage are within the set. Warmth reads negative because
  the teal hose bases fill the brightest tenth of the lower half; the warm
  wedge pool is visible on the wall.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

Author: TMHSDigital

README.md

@@ -735,7 +735,7 @@ toward the core (dot ≥ 0.998).
 </tr>
 <tr>
 <td width="46%" valign="middle">
-<a href="examples/armature-bend/"><img src="examples/armature-bend/preview.webp" alt="Armature bend: three tapered tubes on a dark studio floor showing rest, half, and full curl under a four-bone armature, per-bone weight bands blending teal through amber to coral at the joints" /></a>
+<a href="examples/armature-bend/"><img src="examples/armature-bend/preview.webp" alt="Armature bend: three ribbed bellows hoses on steel foot flanges showing rest, half, and full curl under a four-bone armature, per-bone weight bands blending teal through amber to coral at the joints" /></a>
 </td>
 <td valign="middle">
 

docs/gallery/armature-bend/index.html

@@ -2020,11 +2020,11 @@ <h3><a href="../gn-modifier-inputs/">gn-modifier-inputs</a></h3>
         </article>
         <article class="card mini">
           <a class="card-media" href="../armature-bend/" tabindex="-1" aria-hidden="true">
-            <img src="../assets/armature-bend-hero.webp" alt="Three tapered tubes, coral to amber to teal, standing straight, half curled and fully curled by an armature." width="1280" height="720" loading="lazy" decoding="async" />
+            <img src="../assets/armature-bend-hero.webp" alt="Three ribbed bellows hoses with brass collars on steel foot flanges, banded teal to amber to coral, standing straight, half curled and fully curled by an armature." width="1280" height="720" loading="lazy" decoding="async" />
           </a>
           <div class="card-body">
             <h3><a href="../armature-bend/">armature-bend</a></h3>
-            <p>Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a tapered tube through rest, half, and full curl.</p>
+            <p>Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a ribbed bellows hose through rest, half, and full curl.</p>
           </div>
         </article>
       </div>

docs/gallery/assets/armature-bend-hero.webp

@@ -1639,11 +1639,11 @@ <h3><a href="../usd-export-evaluation-mode/">usd-export-evaluation-mode</a></h3>
         </article>
         <article class="card mini">
           <a class="card-media" href="../armature-bend/" tabindex="-1" aria-hidden="true">
-            <img src="../assets/armature-bend-hero.webp" alt="Three tapered tubes, coral to amber to teal, standing straight, half curled and fully curled by an armature." width="1280" height="720" loading="lazy" decoding="async" />
+            <img src="../assets/armature-bend-hero.webp" alt="Three ribbed bellows hoses with brass collars on steel foot flanges, banded teal to amber to coral, standing straight, half curled and fully curled by an armature." width="1280" height="720" loading="lazy" decoding="async" />
           </a>
           <div class="card-body">
             <h3><a href="../armature-bend/">armature-bend</a></h3>
-            <p>Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a tapered tube through rest, half, and full curl.</p>
+            <p>Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a ribbed bellows hose through rest, half, and full curl.</p>
           </div>
         </article>
         <article class="card mini">

docs/gallery/car-mirror-symmetry/index.html

@@ -2358,11 +2358,11 @@ <h3><a href="../depsgraph-export/">depsgraph-export</a></h3>
         </article>
         <article class="card mini">
           <a class="card-media" href="../armature-bend/" tabindex="-1" aria-hidden="true">
-            <img src="../assets/armature-bend-hero.webp" alt="Three tapered tubes, coral to amber to teal, standing straight, half curled and fully curled by an armature." width="1280" height="720" loading="lazy" decoding="async" />
+            <img src="../assets/armature-bend-hero.webp" alt="Three ribbed bellows hoses with brass collars on steel foot flanges, banded teal to amber to coral, standing straight, half curled and fully curled by an armature." width="1280" height="720" loading="lazy" decoding="async" />
           </a>
           <div class="card-body">
             <h3><a href="../armature-bend/">armature-bend</a></h3>
-            <p>Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a tapered tube through rest, half, and full curl.</p>
+            <p>Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a ribbed bellows hose through rest, half, and full curl.</p>
           </div>
         </article>
         <article class="card mini">

docs/gallery/contact-sheets/armature-bend-contact-sheet.webp

@@ -633,11 +633,11 @@ <h2><a href="grease-pencil-rosette/">grease-pencil-rosette</a></h2>
       </article>
       <article class="card" data-tags="armature depsgraph" data-kind="examples" data-name="armature-bend">
         <a class="card-media" href="armature-bend/" tabindex="-1" aria-hidden="true">
-          <img src="assets/armature-bend-hero.webp" alt="Three tapered tubes, coral to amber to teal, standing straight, half curled and fully curled by an armature." width="1280" height="720" loading="lazy" decoding="async" />
+          <img src="assets/armature-bend-hero.webp" alt="Three ribbed bellows hoses with brass collars on steel foot flanges, banded teal to amber to coral, standing straight, half curled and fully curled by an armature." width="1280" height="720" loading="lazy" decoding="async" />
         </a>
         <div class="card-body">
           <h2><a href="armature-bend/">armature-bend</a></h2>
-          <p class="teaches">Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a tapered tube through rest, half, and full curl.</p>
+          <p class="teaches">Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a ribbed bellows hose through rest, half, and full curl.</p>
           <p class="witnesses"><span class="tag">witnesses</span> edit_bones exists only in edit mode (empty in object mode), vertex groups bind to bones strictly by name, and the armature modifier is exactly linear blend skinning: every evaluated vertex must equal Σ wᵢ·(pose_bone.matrix @ bone.matrix_local.inverted()) @ rest, root ring pinned, tip deflected — a straight tube fails.</p>
           <a class="card-link" href="armature-bend/">View example<span class="sr-only"> armature-bend</span> <span aria-hidden="true">&rarr;</span></a>
         </div>

docs/gallery/depsgraph-export/index.html

@@ -1118,11 +1118,11 @@ <h3><a href="../depsgraph-export/">depsgraph-export</a></h3>
         </article>
         <article class="card mini">
           <a class="card-media" href="../armature-bend/" tabindex="-1" aria-hidden="true">
-            <img src="../assets/armature-bend-hero.webp" alt="Three tapered tubes, coral to amber to teal, standing straight, half curled and fully curled by an armature." width="1280" height="720" loading="lazy" decoding="async" />
+            <img src="../assets/armature-bend-hero.webp" alt="Three ribbed bellows hoses with brass collars on steel foot flanges, banded teal to amber to coral, standing straight, half curled and fully curled by an armature." width="1280" height="720" loading="lazy" decoding="async" />
           </a>
           <div class="card-body">
             <h3><a href="../armature-bend/">armature-bend</a></h3>
-            <p>Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a tapered tube through rest, half, and full curl.</p>
+            <p>Rigging end to end in the data API — edit_bones chain construction, name-bound vertex groups with smoothstep blend zones, posing, and depsgraph evaluation — bending a ribbed bellows hose through rest, half, and full curl.</p>
           </div>
         </article>
         <article class="card mini">

docs/gallery/gltf-skin-roundtrip/index.html

@@ -1,6 +1,6 @@
 # Armature Bend
 
-A runnable example that rigs a tapered, segmented tube with a four-bone armature chain —
+A runnable example that rigs a tapered, ribbed bellows hose with a four-bone armature chain —
 `edit_bones` construction, name-bound vertex groups with smoothstep blend zones, a posed
 curl — and checks the depsgraph-evaluated result against closed-form linear blend
 skinning, following [`mesh-editing-and-bmesh`](../../skills/mesh-editing-and-bmesh/SKILL.md)
@@ -25,9 +25,14 @@ with `VertexGroup.add()` dangles the attribute reference when the deform layer i
 allocated (hard crash on 4.5, silent luck on 5.1), so the script finishes all weight
 writes before creating the color attribute.
 
-The render shows rest → half curl → full curl left to right, with per-bone weight
-bands visualized through a `BoneTint` color attribute — the smooth color blends at the
-joints are the same weights the LBS check asserts.
+The render shows rest → half curl → full curl left to right. The hose is lathed from an
+`(r, z)` profile — brass collars at both ends, a ribbed rubber section between — and every
+weight is a function of `z` alone, so the ribs change nothing the LBS check asserts; they make
+the deformation legible, fanning open on the outside of each bend and crowding on the inside.
+Per-bone weight bands are visualized through a `BoneTint` color attribute on the rib crests
+(a `Crest` attribute darkens the valleys) — the smooth color blends at the joints are the same
+weights the check asserts. Each hose stands on a render-only steel foot flange; the render path
+gates framing through `examples/gallery_framing.py` (exit 10) before writing the still.
 
 ## Run
 
@@ -60,6 +65,7 @@ against it.
 | 7 | Root ring moved |
 | 8 | Tip did not deflect (`--zero-curl` lands here) |
 | 9 | `--output` produced no file |
+| 10 | Framing gate violation on the `--output` path (`gallery_framing`) |
 
 The `blender-smoke` workflow runs the check on Blender 5.2 LTS and 4.5 LTS
 (5.1 on the weekly cron, the `needs-5.1` PR label, or manual dispatch).