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/Standing Forward Fold/motion.json

@@ -5,7 +5,7 @@
   "working": ["leg_r", "leg_l", "spine"],
   "frames": [
     {
-      "hold": 0.4, "tween": 1.2,
+      "hold": 0.5, "tween": 1.8,
       "root": {"pos": [160, 64], "pitch": 5},
       "spine": [0, 0],
       "neck": 2, "head": -6,
@@ -16,16 +16,16 @@
       "pins": {"foot_r": [158, 148], "foot_l": [162, 150]}
     },
     {
-      "hold": 0.6, "tween": 1.2,
-      "root": {"pos": [147, 66], "pitch": 134},
-      "spine": [11, 13],
-      "neck": 16, "head": -56,
-      "shoulder_r": 90, "elbow_r": 6,
-      "shoulder_l": 90, "elbow_l": 6,
-      "hip_r": 34, "knee_r": 14, "ankle_r": 10,
-      "hip_l": 34, "knee_l": 14, "ankle_l": 10,
+      "hold": 0.7, "tween": 1.8,
+      "root": {"pos": [148, 62], "pitch": 80},
+      "spine": [44, 52],
+      "neck": 32, "head": 0,
+      "shoulder_r": {"flexion": 74, "abduction": 9, "rotation": 0}, "elbow_r": 122,
+      "shoulder_l": {"flexion": 71, "abduction": 9, "rotation": 0}, "elbow_l": 121,
+      "hip_r": 87, "knee_r": 4, "ankle_r": 6,
+      "hip_l": 87, "knee_l": 4, "ankle_l": 6,
       "pins": {"foot_r": [158, 148], "foot_l": [162, 150],
-               "hand_r": [159, 151], "hand_l": [163, 152]}
+               "hand_r": [168, 150], "hand_l": [172, 151]}
     }
   ]
 }