diff --git a/docs/proof-of-capabilities.md b/docs/proof-of-capabilities.md
index dd52bcd1..e2a4a7d3 100644
--- a/docs/proof-of-capabilities.md
+++ b/docs/proof-of-capabilities.md
@@ -78,11 +78,18 @@ random or mocked, the hash would not be reproducible.
 ```bash
 python archive/v1/data/proof/verify.py
 # Expect:  VERDICT: PASS
-# Pipeline hash: ca58956c1bbee8c46f1798b3d6b6f1f829aa5db90bba53e07177830eca429199
+# Pipeline hash: f8e76f21a0f9852b70b6d9dd5318239f6b20cbcb4cdd995863263cecdc446f7a
 ```
 
 The published expected hash is committed at `archive/v1/data/proof/expected_features.sha256`.
-Run it on your machine; the hash must match bit-for-bit.
+Run it on your machine — it reproduces **bit-for-bit across platforms** (verified identical on
+Windows, two independent Linux hosts, and the GitHub Azure CI runner). For the one feature that
+*isn't* bit-stable — the peak-normalized Doppler spectrum, whose argmax flips under
+cross-microarchitecture FFT reordering — the proof excludes it from the hash and additionally
+checks every other feature against a committed reference vector within a strict relative tolerance
+(`expected_features_reference.npz`), so a genuine regression still fails while CPU-level float
+noise does not. Five features (amplitude mean/variance, phase difference, correlation matrix, and
+the FFT-based PSD) carry the deterministic proof.
 
 **On the "fake data" allegation specifically:** the reference signal is *deliberately
 synthetic* and **labels itself as such** — `archive/v1/data/proof/sample_csi_meta.json` says: