Gyro: BT_GYRO_TRACE per-frame integrator trace -- oscillation verified vs authored constants (task #56)

25-hit MP autofire trace: kick -> damped oscillation -> settle, peaks well
inside clamps, no NaN/drift; measured Y:X frequency ratio 7.75x matches
sqrt(springK.y/springK.x) exactly.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

context/cockpit-view.md

@@ -118,6 +118,12 @@ inverse(eyeWorld)`. No LookAt anywhere.
   (projweap.cpp FireWeapon: damage>3 → impulse (0,0.6,−1.5) × damage/16, @4bc136-4bc19c).
   Verified live: `[gyro-dmg]` fires per hit with correct scaling, eyePosition shows the damped
   oscillation (ramp to ~0.015u, Y oscillating, decay to 0), no NaN, kill chain un-regressed.
+  **Quantitatively verified (2026-07-11 MP trace):** `BT_GYRO_TRACE=1` logs the integrator state
+  every displaced frame (`[gtrace]`); a 25-hit autofire session (scratchpad/GYRO_TRACE.png)
+  shows per-hit kick → damped oscillation → settle-to-zero-and-stay, peaks ±0.028u X/Z ±0.005u Y
+  (well inside the ±0.1/0.15 clamps), body pitch/roll ±0.02 rad, zero NaN/drift — and the
+  measured frequency ratio matches the authored constants: Y period 9.5 frames vs X/Z ~75 ≈
+  √(springK.y/springK.x)=√60≈7.75× as dictated by springK=(−0.2,−12,−0.2). [T2]
 - **Deferred gyro tail:** (a) the alternate-gait engage JOLT + 0.4s engaged-gait RUMBLE
   (@4aa158-4aa365 — full byte recipe in the wf_6880e605 synthesis; **flagged [T3] on the gate
   naming** and it mutates the gait state machine tasks #49/#50 stabilized — do NOT wire without