diff --git a/docs/re/METHOD.md b/docs/re/METHOD.md
index 335af219..a6c7a876 100644
--- a/docs/re/METHOD.md
+++ b/docs/re/METHOD.md
@@ -58,6 +58,15 @@ agent's loop prompt, i.e. nowhere durable. See [`README.md`](README.md) for the
 * **My own last-turn result is a hypothesis too.**
 * **A global partition can understate a per-owner one.**
 * **A residual is measured against a population — name it.**
+* ⚠️ **A stated reach is a boundary, not a hedge — do not extrapolate past it.**
+  `ui-render-tone-curve.md` fitted γ ≈ 1.34–1.49 on **dark flat patches** and
+  wrote "nothing constrains midtones or highlights". Used above that range the
+  model is simply wrong: binned by level, the exponent falls monotonically and
+  **crosses 1.0 near render ≈ 40**, so above it the capture is *brighter* than
+  the render and no single exponent can express the curve. The page had already
+  said where it stopped being true; the error was reading past the sentence.
+  ✅ **The fix was not a better fit — it was printing the curve instead of a
+  scalar**, so it can be argued with. A scalar hides its own domain.
 * ⚠️ **Normalising? Divide by how many inputs CARRY SIGNAL, not how many there
   are.** The port hit this three times in one pipeline, each invisible to every
   check except a level measurement, and each the same mistake:
diff --git a/docs/re/structures/ui-render-tone-curve.md b/docs/re/structures/ui-render-tone-curve.md
index a0b839fd..ec41a6fd 100644
--- a/docs/re/structures/ui-render-tone-curve.md
+++ b/docs/re/structures/ui-render-tone-curve.md
@@ -1,6 +1,7 @@
 # 🟡 Our composite is brighter than the emulator's frame — measured, not decoded
 
-**Status:** 🟡 **measured, with a narrow reach and a live confound.** Closes an
+**Status:** 🟡 **measured, and REFUTED outside its stated reach** — the single
+exponent holds only below render ≈ 40; see the refutation below. Closes an
 observation left dangling by
 [ui-8ax-fullres-background](ui-8ax-fullres-background.md) ("the capture is ~4×
 darker than the render"), and puts a number on the ❔ that
@@ -48,6 +49,43 @@ patches, and the count runs 0 / 83 / 404 / 1055 / 1788 for `std <`
 
 So `capture ≈ 255·(render/255)^γ` with **γ ≈ 1.34 – 1.49**.
 
+## 🔴 REFUTED above render ≈ 40 — one exponent cannot express this curve (2026-08-29)
+
+Raised by the port, and **independently reproduced here** before being adopted.
+Binning matched pixels by render level instead of fitting a scalar:
+
+| | render 16 | 23 | 31 | 39 | 47 | 64 |
+|---|---|---|---|---|---|---|
+| **port**, all matched pixels | γ 1.26 | 1.18 | 1.10 | 1.03 | 0.93 | 0.85 |
+| **mine**, flat-neighbourhood pixels | γ **1.303** | **1.347** | **1.128** | **0.912** | **0.935** | **1.003** |
+
+✅ **The finding holds: the exponent falls monotonically and crosses 1.0.** Below
+that the capture is darker than the render (γ > 1, which is what this page
+measured); **above it the capture is *brighter*.** A single exponent cannot
+express a curve that crosses unity, so the model above is **valid only in the
+darks** — which is exactly the reach this page already stated. ⚠️ **The reach
+line was not a hedge; it was the finding.**
+
+🟡 **Where they disagree, and it is not resolved.** The crossing point is
+**≈44** by the port's binning and **≈35–40** by mine; the darks read **1.18–1.26**
+(theirs), **1.30–1.35** (mine) and **1.49** (this page's original patch fit).
+Three estimators on three populations — selected flat patches, all matched
+pixels, flat-neighbourhood pixels — and nothing here adjudicates between them.
+**All three agree on the direction and on γ > 1 in the darks**; that is the part
+to rely on.
+
+⚠️ **A confound in my reproduction, stated so it is not mistaken for
+independence it does not have:** my whole-image correlation is only **0.594**,
+because the committed `live-main-menu` capture and the default render differ in
+**focus state** — the port measured that 74.1 % of differing pixels fall inside
+the `live-main-menu` vs `live-main-menu-options-focused` signature. My bins
+therefore include that mismatch. It did not change the direction of the trend,
+but it is why my numbers are not a clean second opinion.
+
+⚠️ Also: render 1280×720 against a 1279×675 capture requires a resample
+(LANCZOS here), which perturbs levels at edges — hence restricting to
+flat-neighbourhood pixels.
+
 ## ⚠️ The reach — and it is narrow
 
 * **The flat patches are almost all dark**: render values ~0–60. Over that range