Add Warm-Up and Stretching activity types

Adds WorkoutActivityType.warmUp (HealthKit .preparationAndRecovery) and
.stretching (.flexibility), and retags the six starter splits that were all
mislabeled as Functional Strength:

- Warm-Up:    Upper Body Warm-Up, Lower Body Warm-Up, Morning Wake-Up
- Stretching: Morning Mobility, Full Body Stretch, Evening Stretch

The split editor's activity picker surfaces them automatically (CaseIterable).
Older app versions decode the new raw values as the default type — additive and
not schema-gated, so no quarantine.

Exercise Library/kinematics.py

@@ -118,6 +118,18 @@ def _clamp(x, lo=-1.0, hi=1.0):
     return max(lo, min(hi, x))
 
 
+# Axial rotation of a two-bone limb is recoverable only from the lower bone's
+# lateral tip; below this magnitude the limb is effectively in-plane and its
+# rotation is left at 0 (see invert_limb).
+ROT_MIN_LATERAL = 0.08
+
+# When a leg's authored knee sits within this fraction of the thigh length off the
+# hip->ankle line (~sin 8.6 deg), the leg is treated as straight and its IK knee is
+# bent anatomically forward rather than trusting the (unreliable) authored side
+# (see solve_limb).
+KNEE_STRAIGHT_FRAC = 0.15
+
+
 # ---------------------------------------------------------------- the frame
 
 # DoF names per joint type; the first is the shorthand a bare number sets.
@@ -296,13 +308,27 @@ def solve_limb(kind, attach, target, guess_mid, lengths, parent, sigma):
 
     along = (a * a + d * d - b * b) / (2 * d)
     h = math.sqrt(max(a * a - along * along, 0.0))
-    best = None
-    for sign in (1.0, -1.0):
+    if kind == "leg":
+        # A knee bends one way only. Near full extension the two knee solutions
+        # straddle the hip->ankle line and the authored guess (also near that line)
+        # cannot reliably pick a side - the bend plane's normal is a cross of two
+        # near-parallel vectors, so its sign is noise and the knee can flip behind
+        # the leg, swinging the whole thigh backward. When the authored knee sits
+        # within KNEE_STRAIGHT_FRAC of the line, treat the leg as straight and bend
+        # the knee anatomically forward (anterior); otherwise honor the authored side.
+        gm = vsub(guess_mid, attach)
+        gm_perp = vsub(gm, vscale(dir_t, vdot(gm, dir_t)))
+        ref = mvec(parent, (1, 0, 0)) if vlen(gm_perp) < KNEE_STRAIGHT_FRAC * a else gm_perp
+        sign = 1.0 if vdot(perp, ref) >= 0 else -1.0
         mid = vadd(attach, vadd(vscale(dir_t, along), vscale(perp, sign * h)))
-        dist = vlen(vsub(mid, guess_mid))
-        if best is None or dist < best[0]:
-            best = (dist, mid)
-    mid = best[1]
+    else:
+        best = None
+        for sign in (1.0, -1.0):
+            mid = vadd(attach, vadd(vscale(dir_t, along), vscale(perp, sign * h)))
+            dist = vlen(vsub(mid, guess_mid))
+            if best is None or dist < best[0]:
+                best = (dist, mid)
+        mid = best[1]
     end = vadd(mid, vscale(vnorm(vsub(target, mid)), b))
     return invert_limb(kind, attach, mid, end, lengths, parent, sigma)
 
@@ -318,9 +344,17 @@ def invert_limb(kind, attach, mid, end, lengths, parent, sigma):
     peel = mtrans(chain(rot_z(flex), rot_x(-sigma * abd)))
     w = vnorm(mvec(peel, mvec(pt, vsub(end, mid))))
     bend = math.degrees(math.acos(_clamp(-w[1])))
-    rot = sigma * math.degrees(math.atan2(w[2], w[0])) if bend > 0.5 else 0.0
+    # Axial rotation is observable only through the lower bone's lateral tip
+    # (w[2]); a near-sagittal limb (w[2] ~ 0) carries no recoverable rotation.
+    # Gating on `bend` alone is too weak: a limb can straighten through this
+    # degeneracy while still visibly bent, and atan2 then snaps to +/-180 on the
+    # sign of a near-zero anterior component - twisting the limb a half-turn and
+    # flipping a pinned hand/foot backward.
+    twist = bend > 0.5 and abs(w[2]) > ROT_MIN_LATERAL
     if kind == "leg":  # knees hinge backward; the sign convention flips
-        rot = sigma * math.degrees(math.atan2(-w[2], -w[0])) if bend > 0.5 else 0.0
+        rot = sigma * math.degrees(math.atan2(-w[2], -w[0])) if twist else 0.0
+    else:
+        rot = sigma * math.degrees(math.atan2(w[2], w[0])) if twist else 0.0
     upper = {"flexion": flex, "abduction": abd, "rotation": rot}
     return upper, {"flexion": bend}