Add standalone numerical verification of all closed forms

README.md

@@ -64,6 +64,16 @@ python experiments/make_figures.py        # rebuilds the figure PDFs from data/
 Each study script is self-contained and writes its JSON into
 `experiments/data/`.
 
+## Independent verification
+
+`experiments/verification/math_verify.py` re-derives every closed form and
+inequality in the manuscript with standalone numpy code (no experiment code
+reused): the relevance identity, the mutual-information correlation, the
+subspace ceiling, the LMMSE receiver against an empirical Wiener solution
+(0.1% MSE agreement; the blind form matches the OFDMA cosine to machine
+precision), and the surrogate bound used in the appendix (uniform constant
+0.97). Results: `experiments/verification/math_verify.json`.
+
 ## Citation and license
 
 To be completed upon acceptance.