theory: prove estimator and innovation regimes

1 files changed, 6 insertions, 0 deletions

diff --git a/ROADMAP.md b/ROADMAP.md
index 70d1649..75efa60 100644
--- a/ROADMAP.md
+++ b/ROADMAP.md
@@ -250,6 +250,12 @@ The minimum theory package contains:
 Numerical simulations must test the predicted scaling with depth, width, directions, perturbation
 scale, and predictor timescale.
 
+**Status: passed on 2026-07-22.** `THEORY.md` gives the exact simultaneous-Rademacher MSE with its
+cross-layer term, the Gaussian layerwise comparison, an `O(sigma^2)` antithetic bias bound, the
+smooth-loss angle/gain/curvature descent condition, the neutral innovation/SNR theorem and
+task-fit absorption result, and a phase/query/work/memory table. `experiments/verify_theory.py`
+checks depth, width, K, sigma, and predictor timescale deterministically; all assertions pass.
+
 ## Protocol discipline
 
 - Hyperparameters are selected on a validation split created only from the training set.