Fix figure IK snapping and gate the library on a fail-hard motion checker

Three solver defects made limbs teleport, twist, or windmill: write-back
angles wrapped at ±180 and lerped the long way around; branch flips landed
on configurations the anatomical write-back cannot represent, silently
pulling pinned extremities off their pins; and the degenerate straight-limb
bend plane fell back to the camera axis instead of the anatomical anterior.
solve_limb now verifies each branch reproduces the solved end before
accepting it, resolve unwraps written-back angles toward the pose they
replace, and the degenerate plane comes from the parent's anterior axis.

render.py --check replays every exercise's full tween loop and fails hard
on six invariants (pin fidelity, continuity, wraps, authored-vs-resolved
drift, ground penetration, resolved ROM); --export refuses to ship a
failing exercise. All 66 motions re-authored or retouched to pass: honest
authored angles where pins used to override them silently, grounded feet
on the seated machines, a vertical bench-press bar path, straight-armed
child's pose, a butterfly stretch seated on the mat, and FK arms where
pins forced impossible reaches. MotionSolver.swift mirrors the solver
changes line for line, held by regenerated fixtures.

Claude-Session: https://claude.ai/code/session_01PKptrgbx74peTwHGRxBojv

Exercise Library/Back Extension/frames/frame-1.svg

@@ -9,8 +9,8 @@
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   <path d="M 58.0 142.0 L 88.0 142.0 L 88.0 142.0 L 58.0 142.0 Z" fill="#c5cad4" stroke="#c5cad4" stroke-width="5" stroke-linecap="round" stroke-linejoin="round"/>
   <g id="arm_l">
-    <path d="M 230.6 141.1 L 200.7 139.0" stroke="#a9afba" stroke-width="5" stroke-linecap="round"/>
-    <path d="M 200.7 139.0 L 222.3 159.5" stroke="#a9afba" stroke-width="5" stroke-linecap="round"/>
+    <path d="M 230.6 141.1 L 209.0 120.5" stroke="#a9afba" stroke-width="5" stroke-linecap="round"/>
+    <path d="M 209.0 120.5 L 198.8 148.3" stroke="#a9afba" stroke-width="5" stroke-linecap="round"/>
   </g>
   <g id="leg_l">
     <path d="M 155.9 102.8 L 113.8 121.1" stroke="url(#grad-leg_l-0)" stroke-width="5.09165" stroke-linecap="round"/>
@@ -20,18 +20,18 @@
   <path id="girdle" d="M 230.6 141.1 L 224.7 141.0 L 224.7 142.9" stroke="#0d9488" stroke-width="5" stroke-linecap="round" stroke-linejoin="round"/>
   <path id="pelvisBar" d="M 155.9 102.8 L 150.0 102.0 L 150.0 103.2" stroke="#0d9488" stroke-width="5" stroke-linecap="round" stroke-linejoin="round"/>
   <path id="spine" d="M 150.0 102.0 Q 192.4 114.2 224.7 141.0" stroke="#0d9488" stroke-width="6" stroke-linecap="round" stroke-linejoin="round"/>
-  <g id="arm_r">
-    <path d="M 224.7 142.9 L 194.8 140.8" stroke="#3a3f4b" stroke-width="6" stroke-linecap="round"/>
-    <path d="M 194.8 140.8 L 216.3 161.4" stroke="#3a3f4b" stroke-width="6" stroke-linecap="round"/>
-  </g>
   <g id="leg_r">
     <path d="M 150.0 103.2 L 110.7 126.8" stroke="#3a3f4b" stroke-width="6" stroke-linecap="round"/>
     <path d="M 110.7 126.8 L 72.0 136.7" stroke="#3a3f4b" stroke-width="6" stroke-linecap="round"/>
     <path d="M 72.0 136.7 L 76.9 146.4" stroke="url(#grad-leg_r-2)" stroke-width="5.96489" stroke-linecap="round"/>
   </g>
+  <g id="arm_r">
+    <path d="M 224.7 142.9 L 203.1 122.4" stroke="#3a3f4b" stroke-width="6" stroke-linecap="round"/>
+    <path d="M 203.1 122.4 L 192.8 150.1" stroke="#3a3f4b" stroke-width="6" stroke-linecap="round"/>
+  </g>
   <circle cx="80.1" cy="142.6" r="4.5" fill="#6b7180"/>
-  <circle id="head" cx="239.1" cy="154.7" r="10" fill="white" stroke="#3a3f4b" stroke-width="6"/>
-  <line id="nose" x1="236.6" y1="164.4" x2="234.9" y2="171.1" stroke="#3a3f4b" stroke-width="4" stroke-linecap="round"/>
+  <circle id="head" cx="241.1" cy="152.3" r="10" fill="white" stroke="#3a3f4b" stroke-width="6"/>
+  <line id="nose" x1="240.2" y1="162.3" x2="239.6" y2="169.1" stroke="#3a3f4b" stroke-width="4" stroke-linecap="round"/>
   <g font-family="-apple-system, Helvetica, sans-serif" font-size="11" fill="#6b7180">
     <line x1="224" y1="16" x2="238" y2="16" stroke="#3a3f4b" stroke-width="4" stroke-linecap="round"/>
     <text x="243" y="20">near</text>

Exercise Library/Back Extension/motion.json

@@ -15,9 +15,9 @@
       "hold": 0.4, "tween": 1.0,
       "root": {"pos": [150, 102], "pitch": 112},
       "spine": [0, 12],
-      "neck": 10, "head": -30,
-      "shoulder_r": 30, "elbow_r": 140,
-      "shoulder_l": 30, "elbow_l": 140,
+      "neck": 1, "head": -30,
+      "shoulder_r": -10, "elbow_r": 114,
+      "shoulder_l": -10, "elbow_l": 114,
       "hip_r": 48, "knee_r": 12, "ankle_r": 12,
       "hip_l": 48, "knee_l": 12, "ankle_l": 12,
       "pins": {"foot_r": [72, 136], "foot_l": [76, 138]}