re(flight): settled turn rates match the definition exactly — withdraw the time-base claim

Re-measured with 5 s of settle per phase and the speed recorded at the moment the
turn starts (flight_law3.py):

  pitch @ 130/s    74.9 deg/s   vs AV_PitchMinus_Min 75
  pitch @ 1821/s   41.1         vs AV_PitchMinus_Max 40
  roll  @ 110/s   129.5         vs AV_Roll_Min 200
  roll  @ 1722/s  149.3         vs AV_Roll_Max 125

Pitch lands on the definition's own numbers with NO scale factor, so the ~1.2x I
attributed to the emulated time base two iterations ago was an artefact of
differentiating during the AA_* acceleration ramp with too little settle. That
explanation is withdrawn: AV_* can be used verbatim.

What remains is only on the linear side — settled speeds still read high and vary
between runs (RT full: 1342 in one flight, 1821 in another, vs MaximumVelocity 1200),
consistent with a craft being shoved around in a firefight. The HUD reads exactly
CruisingVelocity at neutral. A clean linear measurement needs a quiet map; no cause
is claimed until then.

Roll re-measured with proper settles confirms the axis difference: no speed
dependence, both regimes near AV_Roll_Max, where pitch moved 75 -> 40.

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

docs/re/captures/turn-law-settled.csv

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+roll_fast,3.915,-0.41609751831590275,0.29451533035891825,-0.8603043504684399
+roll_fast,3.965,-0.41609751831590275,0.29451533035891825,-0.8603043504684399

docs/re/flight-speed-law.md

@@ -83,7 +83,7 @@ Two claims of the field names are confirmed:
 * **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+## The ~1.2× factor — ⚠️ WITHDRAWN, see "Settled rates match exactly" below
 
 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
@@ -222,3 +222,42 @@ not perfectly separated pair of regimes.
 
 Raw samples: [`captures/throttle-curve-lt.csv`](captures/throttle-curve-lt.csv) ·
 [`captures/turn-law-roll.csv`](captures/turn-law-roll.csv).
+
+---
+
+# ⚠️ Settled rates match the definition EXACTLY — the "time base" reading is withdrawn
+
+The earlier turn measurements settled each phase for 1.5 s and then differentiated
+from the first second. Re-running with **5 s of settle** and the craft's speed
+recorded *at the moment the turn starts*
+([`tools/re-capture/flight_law3.py`](../../tools/re-capture/flight_law3.py)):
+
+| phase | speed at turn | measured rate | definition |
+|---|---|---|---|
+| pitch, minimum speed | 130 /s | **74.9 °/s** | `AV_PitchMinus_Min` **75** |
+| pitch, half throttle | 388 /s | 73.7 °/s | (between, see below) |
+| pitch, maximum speed | 1 821 /s | **41.1 °/s** | `AV_PitchMinus_Max` **40** |
+| roll, minimum speed | 110 /s | 129.5 °/s | `AV_Roll_Min` 200 |
+| roll, maximum speed | 1 722 /s | 149.3 °/s | `AV_Roll_Max` 125 |
+
+**Pitch lands on 75 and 40 — the definition's own numbers, with no scale factor.**
+So the ~1.2× I attributed to the emulated time base was an artefact of measuring
+during the `AA_*` acceleration ramp with too little settle, and that explanation is
+**withdrawn**: angular rates need no correction, and a reimplementation should use
+`AV_*` verbatim.
+
+What remains unexplained is only on the **linear** side: settled speeds still read
+high and vary between runs (`RT` full measured 1 342 in one flight and 1 821 in
+another, against `MaximumVelocity` 1 200), which is what a craft being shoved around
+in a firefight looks like. The HUD, meanwhile, reads exactly `CruisingVelocity` at
+neutral throttle. A clean linear measurement wants a quiet corner of a map, not this
+one — until then, no cause is claimed.
+
+**Roll, re-measured with proper settles, confirms the axis difference**: 129.5 at
+110 /s and 149.3 at 1 722 /s — no speed dependence, both near `AV_Roll_Max` **125**,
+where pitch moved 75 → 40 across the same range. The mid-throttle pitch point does
+not discriminate lerp-versus-switch, because at half throttle the craft only reached
+388 /s, where an interpolation would predict ~66 °/s against a measured 73.7 — inside
+this probe's noise.
+
+Raw samples: [`captures/turn-law-settled.csv`](captures/turn-law-settled.csv).

tools/re-capture/flight_law3.py

@@ -0,0 +1,82 @@
+#!/usr/bin/env python3
+"""Is the `_Min`/`_Max` pair a LERP on speed, and is roll really speed-independent?
+
+Pitch measured 87 deg/s at minimum speed and 54 at maximum, against
+`AV_PitchMinus_{Min,Max}` 75/40 — consistent with either a two-state switch or an
+interpolation. A THIRD point settles it: at half throttle the craft sits midway
+between cruise and maximum, so an interpolation must put the pitch rate between the
+two, while a switch cannot.
+
+Roll measured ~144 and ~150 in the two regimes, but only 2 s apart — not enough
+settle for a 126 -> 1342 speed change. Here every phase settles 5 s.
+
+Usage: flight_law3.py <out.csv> [dwell_s]
+"""
+import json, math, os, struct, subprocess, sys, time
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+import speed_law
+
+SETTLE = 5.0
+
+def pad(*a):
+    subprocess.run(["vgamepad", *a], capture_output=True)
+
+def row_at(fd, off, cfg, row):
+    at = off + cfg["rot_delta"] + row * cfg["rot_stride"]
+    v = struct.unpack(">3f", os.pread(fd, 12, at))
+    n = math.sqrt(sum(c * c for c in v)) or 1.0
+    return tuple(c / n for c in v)
+
+def ang(a, b):
+    return math.degrees(math.acos(max(-1.0, min(1.0, sum(a[i] * b[i] for i in range(3))))))
+
+def main():
+    out_csv = sys.argv[1]
+    dwell = float(sys.argv[2]) if len(sys.argv) > 2 else 4.0
+    cfg = json.load(open("/tmp/nav-live.json"))
+    w, off, nm = speed_law.find_player()
+    if not w:
+        sys.exit("player entity not found after retries")
+    print(f"# locked on {nm}")
+    fwd, other = cfg.get("fwd_row", 0), (1 if cfg.get("fwd_row", 0) != 1 else 2)
+    rows = []
+    phases = [
+        # label,        throttle,        stick,        matrix row to watch
+        ("pitch_slow",  ("LT", 1.0),  ("LY", 1.0),  fwd),
+        ("pitch_mid",   ("RT", 0.5),  ("LY", 1.0),  fwd),
+        ("pitch_fast",  ("RT", 1.0),  ("LY", 1.0),  fwd),
+        ("roll_slow",   ("LT", 1.0),  ("LX", 1.0),  other),
+        ("roll_fast",   ("RT", 1.0),  ("LX", 1.0),  other),
+    ]
+    for label, (trig, tv), (axis, av), row in phases:
+        pad("trig", "RT", "0.0"); pad("trig", "LT", "0.0")
+        pad("axis", "LX", "0.0"); pad("axis", "LY", "0.0")
+        pad("trig", trig, str(tv))
+        time.sleep(SETTLE)                      # 5 s: a full 126 -> 1342 change needs ~2 s
+        # speed at the moment of the turn, so the regime is recorded not assumed
+        p0 = speed_law.pos_at(w.fd, off); time.sleep(0.6); p1 = speed_law.pos_at(w.fd, off)
+        v_at_turn = math.dist(p0, p1) / 0.6
+        pad("axis", axis, str(av))
+        seq, t0 = [], time.time()
+        while time.time() - t0 < dwell:
+            seq.append((round(time.time() - t0, 3), *row_at(w.fd, off, cfg, row)))
+            time.sleep(0.05)
+        pad("axis", axis, "0.0")
+        rows += [(label, *s) for s in seq]
+        rates = []
+        for t in range(int(dwell) - 1):
+            a = [s for s in seq if s[0] >= t][0]
+            b = [s for s in seq if s[0] <= t + 1][-1]
+            rates.append(ang(a[1:], b[1:]) / (b[0] - a[0]))
+        mean = sum(rates) / len(rates)
+        print(f"# {label:<11} speed {v_at_turn:6.0f}/s   rate {mean:6.1f} deg/s   " +
+              " ".join(f"{r:5.0f}" for r in rates))
+    pad("trig", "RT", "0.0"); pad("trig", "LT", "0.0"); pad("reset")
+    with open(out_csv, "w") as f:
+        f.write("phase,t,ax,ay,az\n")
+        for r in rows:
+            f.write(",".join(str(x) for x in r) + "\n")
+    print(f"# wrote {out_csv}")
+
+if __name__ == "__main__":
+    main()