Body Stage 1 collapse root-caused + fixed: NaN in torso servo math (GetAngle = 2*acos(W) at W=1.0000001), not solver stacking

- BodyMath.RotationError: atan2-based shortest-arc error (no NaN, no GetAxis gain collapse
  inside 0.16 deg); used by PhysicsTorso orientation servo and PhysicsHands rotation lock
- BodyMath.ResetIfNonFinite escape hatch on torso + hands
- PhysicsHands.Drive extracted (static) so spikes run the real hand chase
- CollapseSpike: deterministic repro (slow yaw drift across a parked chest, 7/40 NaN on old
  code) + solver-stacking scenarios (seated chest in table, two-hand-welded 50 kg anvil,
  real PropShop) — 49/49 clean after fix, x3; all other spikes PASS x3
- Failure brief RESOLUTION section; HANDOFF/AGENTS updated

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

research/body-stage1-failure-brief.md

@@ -1,5 +1,8 @@
 # Body Stage 1 failure brief — chest collapse in-headset (2026-10-01)
 
+**STATUS: RESOLVED — root cause = NaN in the torso orientation servo math (not the solver).
+See the RESOLUTION section at the end. The hypotheses below are kept as the record.**
+
 SELF-CONTAINED brief for an external agent (zero project context assumed). Godot 4.7.2 mono,
 C#, PCVR at 90 Hz (physics tick = 90), physics engine = **Box3D** (bearlikelion's
 `godot-box3d` GDExtension — a full PhysicsServer3D replacement; locally patched so Godot's
@@ -127,3 +130,46 @@ the prop table in chaos (props piled/thrown, panel knobs displaced). Log
 
 Owner directive: painlessness bar = no multi-iteration fundamental sagas. Deliver the
 analysis, the repro, and the smallest honest fix — the owner playtests feel afterwards.
+
+## RESOLUTION (2026-10-01, same day) — root cause found, deterministic repro, fixed
+
+**The NaN was script math, not the solver.** H1–H3 were all tested headless and did NOT
+reproduce (`scenes/collapse_spike.tscn`, stacking family: chest 5/15 cm into the static
+table, 50 kg anvil rigid-welded to two 90 N chase hands, the exact logged grab sequence,
+the real PropShop with the chest plowing through props — all finite).
+
+Root cause, verified step by step:
+1. The orientation servo computed `qErr.GetAngle()` = `2*acos(W)`. Godot C#'s `Mathf.Acos`
+   is UNCLAMPED (docs: input "must be" in [-1, 1]); when float rounding puts the error
+   quaternion's W at **1.0000001**, the angle is NaN. `Mathf.Min(NaN, cap)` passes NaN
+   through, the slew clamp's `wErr.Length() > max` is false for NaN, and
+   `AngularVelocity += NaN` goes straight into Box3D (`b3Body_SetAngularVelocity` only
+   asserts validity in debug builds). The chest transform goes NaN → renderer flood →
+   arm visuals (derived from the chest pose) vanish with it → "head detached from body".
+2. Why it needed a seated, still player: `Quaternion.GetAxis()` returns the RAW
+   un-normalized xyz once W > 1 − 1e-6 (angle < ~0.16°), so the servo's gain collapsed
+   ~1000× inside that band — the body parked a fraction of a degree off target. The
+   rounding hazard (error < ~3e-4 rad) is only reached when the yaw target then DRIFTS
+   SLOWLY across that parked yaw — exactly a seated player holding still (the 50 kg anvil
+   welded to both hands can't move: 2×90 N < 0.95×490 N friction, hence the logged
+   0.01 m/s releases). Normal motion crosses the band too fast. The hands and anvil stayed
+   finite (they kept grabbing after the flood), consistent with a torso-only NaN.
+3. Deterministic repro: head still at 40 yaws, target drifting 0.2°/s → **7/40 scenarios
+   NaN the chest** on the old code (W = 1.0000001 at the crossing tick, body w = 0).
+
+Fix (`scripts/BodyMath.cs`): `RotationError()` = shortest-arc axis·angle via
+`2*atan2(|xyz|, W)` with a properly normalized axis — exact near zero, can't leave its
+domain. Used by the torso servo AND the hand rotation lock (hands were not observed to NaN
+— their Basis-product path measured 0/200k — but shared the gain collapse). Escape hatch:
+`BodyMath.ResetIfNonFinite()` on every driven body (torso, hands) — any future non-finite
+state resets that body onto its target with a warning instead of poisoning the renderer.
+After the fix: collapse spike 49/49 clean ×3, yaw error under slow drift 0.026° (was a
+0.16° stall); physics/weld/grab/body spikes all PASS ×3.
+
+Mitigations M1–M4 were NOT needed for the NaN. Side observations kept for the owner:
+- The prop "table chaos" is real and separate: a seated chest sweeping the table plows
+  props off at up to ~3.8 m/s (2400 N body) — honest physics, tune by feel if unwanted.
+- Seated calibration: head height 1.01 m clamps arm length to the 0.50 m minimum, so
+  reaching saturates `ReachOffset` (0.25 m) and leans the chest INTO the table. The chest
+  then rests saturated on the table edge — stable in every repro, but a calibration that
+  assumes standing height is the deeper issue (see HANDOFF known issues).