re: a bank's wave 1 is not a filtered copy of wave 0 -- and my own discriminator cannot finish the job

Coherence on BGM_103, the menu's bank, with controls run first: a real linear
filter of wave 0 reads 0.93-0.94 in every band, a different bank reads 0.001, and
wave 0 misaligned by 1 s reads 0.004-0.057. The measurement reads 0.027 at 1-4 kHz,
so the 'wave 1 is wave 0 filtered' model is refuted.

The frequency structure is inverted relative to any mic-pair or reverb model:
coherence rises with frequency (0.169 -> 0.827) while energy falls (71 % -> 0.2 %),
and a rear pair decorrelates fastest at HF. In the midrange the two waves are 13x
further apart than the two channels of one wave.

But the L-R control is what limits the tool and it is recorded as such: within one
wave, genuinely one performance in two channels, coherence is only 0.221-0.497. So
'same performance' does not imply high coherence here, my positive control was the
wrong model of the rear-pair reading, and the 🟡 is NOT settled. The tool tests for
linear filtering and neither surviving reading requires it.

Also corrects MISSION's Q10 row, which still carried the refuted three-sub-wave
premise and had directed work at a dead question for days. Its gate is in fact met.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Wuu56cE8vJGTBtn1ppsk8v

docs/re/structures/bgm-two-stems.md

@@ -92,6 +92,47 @@ twice, the second time as a bass-less secondary stem.
   decorrelated between L and R, and with the bass managed away to the front pair.
 * **A second intensity layer** to be mixed in or crossfaded.
 
+### ❌ One of the two is now narrowed: wave 1 is NOT a filtered copy of wave 0
+
+**measured 2026-08-30** — [`../data/bgm-stem-coherence.txt`](../data/bgm-stem-coherence.txt),
+`tools/re-capture/bgm_stem_coherence.py`, on **`BGM_103`**, the menu's bank.
+
+Magnitude-squared coherence is ~1 wherever one signal is a **linear filter** of
+the other. Controlled first: a real filter of wave 0 reads **0.93–0.94** in every
+band, a different bank reads **0.001**, and wave 0 against itself misaligned by
+1 s reads **0.004–0.057**.
+
+| band | w0 vs w1 | w0's own L vs R | energy in w0 |
+|---|---|---|---|
+| 0–200 Hz | 0.169 | 0.321 | 71.4 % |
+| 200 Hz–1 kHz | 0.184 | 0.221 | 24.8 % |
+| **1–4 kHz** | **0.027** | **0.363** | 2.4 % |
+| 4–12 kHz | 0.635 | 0.445 | 1.0 % |
+| 16–24 kHz | 0.827 | 0.450 | 0.2 % |
+
+❌ **"Wave 1 is wave 0 filtered" is dead.** A filter reads 0.936 at 1–4 kHz; the
+measurement reads **0.027**.
+
+📌 **The frequency structure is inverted** relative to any mic-pair or reverb
+model: coherence *rises* with frequency while energy *falls*. A rear pair or a
+reverb return decorrelates fastest at HF. Whatever is coherent lives in bands
+holding ~1.3 % of the energy; the bands holding 96 % of it read 0.169 and 0.184.
+
+📌 **In the midrange the two waves are 13× further apart than the two channels of
+one wave** — 0.027 against 0.363.
+
+🔴 **But the same control kills the clean answer, so this does NOT settle the
+🟡.** L vs R *within* one wave is genuinely one performance in two channels, and
+it reads only **0.221–0.497** — nowhere near 0.94. So in this material "same
+performance" does not imply high coherence, and my positive control was the wrong
+model of the rear-pair reading: a real 4-channel mix's rear pair is not a linear
+filter of its front pair. **The tool tests for linear filtering, and neither
+surviving reading requires it.** Stated here rather than discovered later.
+
+⚠️ Reach: one bank, one 60 s window, mono-summed. The 16–24 kHz reading of 0.827
+is unexplained and is *not* generic codec behaviour — the different-bank control
+reads 0.002 in that same band.
+
 **Not settled, and the obvious field does not settle it.** `ChannelMask` is
 `0x0002` on *both* waves, and [`sound-slb.md`](sound-slb.md) already records that
 this game writes meaningless channel metadata (movie voices declare 2 channels