web: the four tonal knobs are sized by what the eye can see, and the highlight head is squared so a bigger rate fits inside the cube

The report was "giá trị thay đổi của các thông số quá nhỏ, không thể hiện được
trên thị giác của ảnh" — at the doc's own rates a full +100 was worth 0.060 of
luma on BLACKS, 0.082 on HIGHLIGHTS and 0.042 on WHITES, and the probe that ran
the frame through the pass read BLACKS +100 moving its mean by 0.0001. Every
rate below is now the largest its own move allows, measured rather than
inherited: 0.058 -> 0.080 on BLACKS, 0.082 -> 0.113 on HIGHLIGHTS and 0.042 ->
0.080 on WHITES, with SHADOWS' 0.151 left where it was because it already bit.

  - `TONE_BLACK_LIFT` 0.7 -> 0.93. The ceiling is a FOLD, not a slope: past
    0.9387 the doc's own square root carries luma backwards inside its window
    (0.94 folds 3.4e-6, 0.95 folds 8.9e-5) and a gradient wears it as a band.
    0.93 is the last round rate under it — monotone on the check's 1/32768
    grid, and the 1e-4 of travel between it and 0.94 is not a code value.
  - `TONE_BLACK_CRUSH` 0.85 -> 8.0. The doc's own form — `L * (1 + amount * W
    * 0.85)` — is bounded by its own window, which is 1 only AT the floor, so
    its whole visible travel at full -100 is 0.019 of luma: five code values on
    a black patch, and a rate past 1 drives the product negative and clips the
    toe to a flat black instead of deepening it. The toe's own EXPONENT,
    `L -> W * (L/W)^(1 + rate * W)`, is monotone for ANY rate and worth 0.054,
    while x = 0 stays on 0 and the 0.18 edge stays on 1 — both anchors and the
    compact support kept.
  - `TONE_HIGH_GAIN` 2.5 -> 14.0, with the head term moved from `(1 - L)` to
    `(1 - L)^2`. The linear headroom dies too slowly to keep the rate's own
    ceiling off the clamp: above a gain worth 2.6 the move overshoots 1.0, the
    clamp draws a plateau and the ramp falls back over it by 0.018 — the fold
    the knee check now measures as a drawdown from the running maximum. Squared,
    the move has died out by the time the ramp reaches the clamp: 14.0 is
    fold-free at both signs and still lands 1.44x of the 1.5x the quarter it
    owns is allowed.
  - `TONE_WHITE_GAIN` 1.5 -> 3.0, which takes the top of the ramp TO the
    ceiling from 0.92 up and leaves the clamp to flatten what is left. That is
    the doc's own §2.4, where a WHITE is the frame's clipping point ("giới hạn
    cháy sáng") and not a Hermite that cannot move the head; it is felt only
    above the 0.80 shoulder and the head is still exactly 1.0 on 1.0.

`FILM_TONE` is re-solved for the squared head, which is worth less at the 0.75
knot for the same rate: monochrome -0.16 -> -0.1143 and mono-high-contrast
+0.83 -> +0.5929. The four knots the stocks are tuned to do not move — 0.22 and
0.7375 on Acros, 0.17 and 0.815 on Acros HC — and the check pins each of them.

The knee check's guard is REPLACED. The old one compared the first cell of the
sweep against the second (a slope at 1/512), which is blind to a fold that
starts later: it passed a ramp whose own drawdown was 0.018. The new one walks
1/32768 of the ramp and measures `running max - value` for each knob at both
signs, over the four moves alone and then over a 243-combination sweep, so what
is pinned is the fold itself and where it is.

Two folds are pinned rather than removed, both named in the check:

  - SHADOWS -100 dips 0.018 (4.6 code values) around 0.06..0.11 of its own
    accord. It is the doc's §2.2 formula — `L *= 1 + amount * W * (1 - L)^1.8`
    — where the window rises faster than the light, and it PREDATES this change.
    The monotone rewrite (`L' = 1 - (1 - L)^(1 - SH * |a| * W(L))`) is written
    out beside it and was NOT taken: it is exact but it costs the knob 30-50% of
    its crush.
  - WHITE +100 rests a plateau on the clamp from 0.92 up. That is what §2.4 asks
    of the knob and the ramp is non-decreasing through it, so it is not a fold.

`scripts/tone-base-check.mjs`'s mirror of the pass takes the same three moves
(its own `toneBlack` and the squared head) so the pixel it predicts is still the
pixel the pass draws.

Checked: node scripts/highlight-knee-check.mjs; node scripts/tone-base-check.mjs;
node scripts/auto-tone-check.mjs; node scripts/half-check.mjs; node
scripts/mask-wb-check.mjs; node scripts/preview-match-check.mjs; node
scripts/raw-develop-check.mjs; node scripts/white-level-check.mjs; node
scripts/wb-table-check.mjs; node scripts/sharpen-check.mjs; node
scripts/denoise-check.mjs; npx tsc --noEmit.

docker/frontend/scripts/tone-base-check.mjs

@@ -107,20 +107,28 @@ const toneWhiteW = (L) => {
   const u = clamp01((L - TONE_WHITE_EDGE) / (1 - TONE_WHITE_EDGE));
   return u * u;
 };
+// toneBlack, as the shader emits it: the lift is the doc's own, the crush is the
+// toe's EXPONENT (monotone for any rate, and the only form that moves a visible
+// amount inside a window that is 1 only at the floor).
+const toneBlack = (L, bl) => {
+  const q = toneBlackW(L);
+  if (bl > 0) return L + TONE_BLACK_LIFT * bl * q * (Math.sqrt(L) - L);
+  return L >= TONE_BLACK_EDGE
+    ? L
+    : TONE_BLACK_EDGE * (L / TONE_BLACK_EDGE) ** (1 + TONE_BLACK_CRUSH * -bl * q);
+};
 // toneCurve, move for move, with the clamp the shader puts after each one.
 // `afterBlack` is the L the SHADOW move reads.
 function toneCurve(L, bl, sh, hl, wh) {
   let q = toneBlackW(L);
-  L = bl > 0
-    ? L + TONE_BLACK_LIFT * bl * q * (Math.sqrt(L) - L)
-    : L * Math.max(1 + TONE_BLACK_CRUSH * bl * q, 0);
+  L = toneBlack(L, bl);
   L = clamp01(L);
   const afterBlack = L;
   q = toneShadowW(L);
   L *= 1 + sh * q * (1 - L) ** 1.8;
   L = clamp01(L);
   q = toneHighW(L);
-  L += TONE_HIGH_GAIN * hl * q * Math.max(L - 0.5, 0) ** 1.5 * (1 - L);
+  L += TONE_HIGH_GAIN * hl * q * Math.max(L - 0.5, 0) ** 1.5 * (1 - L) * (1 - L);
   L = clamp01(L);
   q = toneWhiteW(L);
   L += TONE_WHITE_GAIN * wh * q * (1 - L) * L;