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/Child's Pose/motion.json

@@ -5,25 +5,25 @@
   "frames": [
     {
       "hold": 2.4, "tween": 2.0,
-      "root": {"pos": [201, 108], "yaw": 180, "pitch": 89},
+      "root": {"pos": [201, 104], "yaw": 180, "pitch": 87},
       "spine": [15, 20],
-      "neck": 15, "head": -13,
+      "neck": 25, "head": -13,
       "shoulder_r": 168, "elbow_r": 8,
       "shoulder_l": 168, "elbow_l": 8,
       "hip_r": 86, "knee_r": 104, "ankle_r": -52,
       "hip_l": 86, "knee_l": 104, "ankle_l": -52,
-      "pins": {"hand_r": [80, 150], "hand_l": [84, 151]}
+      "pins": {"hand_r": [72, 151], "hand_l": [66.5, 151]}
     },
     {
       "hold": 2.6, "tween": 2.0,
-      "root": {"pos": [202, 110], "yaw": 180, "pitch": 92},
+      "root": {"pos": [202, 103], "yaw": 180, "pitch": 84},
       "spine": [16, 22],
-      "neck": 17, "head": -15,
+      "neck": 36, "head": -15,
       "shoulder_r": 172, "elbow_r": 6,
       "shoulder_l": 172, "elbow_l": 6,
       "hip_r": 90, "knee_r": 108, "ankle_r": -52,
       "hip_l": 90, "knee_l": 108, "ankle_l": -52,
-      "pins": {"hand_r": [78, 150], "hand_l": [82, 151]}
+      "pins": {"hand_r": [73.3, 151], "hand_l": [67.9, 151]}
     }
   ]
 }