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/Butterfly Stretch/motion.json

@@ -1,30 +1,119 @@
 {
   "name": "Butterfly Stretch",
   "primary": 2,
-  "camera": {"yaw": 52},
-  "working": ["leg_r", "leg_l"],
+  "camera": {
+    "yaw": 52
+  },
+  "working": [
+    "leg_r",
+    "leg_l"
+  ],
   "frames": [
     {
-      "hold": 2.2, "tween": 1.8,
-      "root": {"pos": [160, 118], "pitch": 4},
-      "spine": [20, 18],
-      "neck": 12, "head": -14,
-      "shoulder_r": {"flexion": 94, "abduction": 12}, "elbow_r": 40,
-      "shoulder_l": {"flexion": 94, "abduction": 12}, "elbow_l": 40,
-      "hip_r": {"flexion": 82, "abduction": 38, "rotation": 44}, "knee_r": 108,
-      "hip_l": {"flexion": 82, "abduction": 38, "rotation": 44}, "knee_l": 108,
-      "pins": {"hand_r": [178, 158], "hand_l": [198, 159]}
+      "hold": 2.2,
+      "tween": 1.8,
+      "root": {
+        "pos": [
+          160,
+          143
+        ],
+        "pitch": 5
+      },
+      "spine": [
+        24,
+        18
+      ],
+      "neck": 6,
+      "head": -8,
+      "shoulder_r": {
+        "flexion": 45.5,
+        "abduction": 25.1,
+        "rotation": 0.0
+      },
+      "elbow_r": 2.0,
+      "shoulder_l": {
+        "flexion": 31.0,
+        "abduction": 40.4,
+        "rotation": -67.7
+      },
+      "elbow_l": 63.5,
+      "hip_r": {
+        "flexion": 120,
+        "abduction": 35,
+        "rotation": 50
+      },
+      "knee_r": 128,
+      "ankle_r": 0,
+      "hip_l": {
+        "flexion": 120,
+        "abduction": 35,
+        "rotation": 50
+      },
+      "knee_l": 128,
+      "ankle_l": 0,
+      "pins": {
+        "hand_r": [
+          162,
+          134
+        ],
+        "hand_l": [
+          209,
+          128
+        ]
+      }
     },
     {
-      "hold": 2.4, "tween": 1.8,
-      "root": {"pos": [160, 118], "pitch": 4},
-      "spine": [26, 24],
-      "neck": 14, "head": -16,
-      "shoulder_r": {"flexion": 98, "abduction": 12}, "elbow_r": 34,
-      "shoulder_l": {"flexion": 98, "abduction": 12}, "elbow_l": 34,
-      "hip_r": {"flexion": 82, "abduction": 44, "rotation": 46}, "knee_r": 110,
-      "hip_l": {"flexion": 82, "abduction": 44, "rotation": 46}, "knee_l": 110,
-      "pins": {"hand_r": [176, 159], "hand_l": [200, 160]}
+      "hold": 2.4,
+      "tween": 1.8,
+      "root": {
+        "pos": [
+          160,
+          143
+        ],
+        "pitch": 5
+      },
+      "spine": [
+        28,
+        21
+      ],
+      "neck": 8,
+      "head": -10,
+      "shoulder_r": {
+        "flexion": 40.4,
+        "abduction": 33.1,
+        "rotation": -24.7
+      },
+      "elbow_r": 18.7,
+      "shoulder_l": {
+        "flexion": 32.1,
+        "abduction": 48.3,
+        "rotation": -70.7
+      },
+      "elbow_l": 80.6,
+      "hip_r": {
+        "flexion": 120,
+        "abduction": 35,
+        "rotation": 50
+      },
+      "knee_r": 128,
+      "ankle_r": 0,
+      "hip_l": {
+        "flexion": 120,
+        "abduction": 35,
+        "rotation": 50
+      },
+      "knee_l": 128,
+      "ankle_l": 0,
+      "pins": {
+        "hand_r": [
+          162,
+          134
+        ],
+        "hand_l": [
+          209,
+          128
+        ]
+      }
     }
   ]
 }