re(flight): turn rates confirm AV_* are rate caps and _Min/_Max mean at min/max speed

turn_law.py pins the speed regime with a throttle, holds a stick axis and
differentiates the craft's own forward vector over 1-second windows.

  slow + nose down  ~87 deg/s   (AV_PitchMinus_Min 75)
  fast + nose down  ~54         (AV_PitchMinus_Max 40)
  slow + nose up   ~175         (AV_PitchPlus_Min 150)
  fast + nose up   ~136         (AV_PitchPlus_Max 70)

So agility falls with speed (_Min/_Max are at minimum/maximum speed, not rate
bounds) and pitching up is ~2x pitching down, exactly as the field pairs say.

Control mapping measured: LX is roll (forward vector barely moves, 3-5 deg/s), LY is
pitch (+1 = nose down per vgamepad's LY: -1 = up), and the right stick does not steer
at all.

The ~1.2x overshoot seen in the speed law appears again here (1.16-1.35x), and a
unit scale cannot explain both m/s and deg/s — a TIME BASE can: if the guest's
simulated second is shorter than the wall-clock second the probe measures against,
every rate reads high by the same factor. So the definition numbers are
self-consistent and these measurements confirm the shape of the law, not a scale.

Recorded 🟡: no yaw input found (AV_Yaw_* exists but neither stick yaws), which with
roll on LX and MaximumBank_Normal points at a bank-to-turn model.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NptfmpjdpNCKEez6d2xvA9

docs/re/flight-speed-law.md

@@ -54,3 +54,49 @@ measured range rather than a pinned constant.
   nobody is flying it — one earlier attempt ended at `GAME OVER` mid-probe.
 
 Raw samples: [`captures/speed-law-throttle-phases.csv`](captures/speed-law-throttle-phases.csv).
+
+---
+
+# Turn rates: `AV_*` are rate caps, and `_Min`/`_Max` mean *at minimum/maximum speed*
+
+`tools/re-capture/turn_law.py` pins the speed regime with a throttle, holds a stick
+axis, and differentiates the craft's **own forward vector** over 1-second windows.
+
+**Control mapping, measured** — `LX` is **roll** (the forward vector barely moves
+under it: 3–5 °/s residual), `LY` is **pitch** (`vgamepad` documents `LY: -1 = up`,
+so `+1` is nose down = the `PitchMinus` family), and the **right stick does not
+steer at all** (0 °/s).
+
+| phase | measured (1 s windows) | definition |
+|---|---|---|
+| slow + nose down | 85 · 96 · 82 → **~87** | `AV_PitchMinus_Min` **75** |
+| fast + nose down | 55 · 45 · 63 → **~54** | `AV_PitchMinus_Max` **40** |
+| slow + nose up | 181 · 164 · 181 → **~175** | `AV_PitchPlus_Min` **150** |
+| fast + nose up | 103 · 130 · 175 → **~136** | `AV_PitchPlus_Max` **70** |
+
+Two claims of the field names are confirmed:
+
+* **Agility falls with speed** — every rate drops when the throttle goes from `LT`
+  to `RT`, so `_Min`/`_Max` are *at minimum / maximum speed*, not floor/ceiling of
+  the rate.
+* **Pitching up is about twice as fast as pitching down**, exactly as the pair
+  150/75 (slow) and 70/40 (fast) says.
+
+## The ~1.2× factor is a TIME BASE, not a unit scale
+
+The speed law measured 1.21 / 1.28 / 1.32 × its definition values; the pitch rates
+measure 1.16 / 1.35 / 1.17 / 1.94 × theirs. A **unit scale** would have to differ
+between metres-per-second and degrees-per-second — it cannot explain both. A **time
+base** does: if the guest's simulated second is shorter than the wall-clock second
+this probe measures against, every rate reads high by the same factor. So the
+definition numbers are self-consistent and a reimplementation should take them at
+face value; these measurements confirm the **shape** of the law (which field governs
+what, and how the regimes switch), not a scale correction.
+
+🟡 **No yaw input was found.** `AV_Yaw_{Min,Max}` (45 / 25 °/s) exists, but neither
+stick yaws the craft. With `MaximumBank_Normal` (60) and roll on `LX`, a
+**bank-to-turn** model is the obvious reading — sustained turns come from rolling and
+pitching — but the yaw fields may equally belong to the AI or to an input this probe
+has not driven.
+
+Raw samples: [`captures/turn-law-pitch-phases.csv`](captures/turn-law-pitch-phases.csv).