baseline: add residual response mirroring

1 files changed, 22 insertions, 0 deletions

diff --git a/THEORY.md b/THEORY.md
index 7038969..c64eb46 100644
--- a/THEORY.md
+++ b/THEORY.md
@@ -291,6 +291,28 @@ mean/minimum feedback-forward cosine `0.9887/0.9661`, norm ratios
 `[0.9537,1.0444]`, and zero forward-parameter access error in the update.
 These are mechanics, not task evidence. A frozen comparator gate is required.
 
+The frozen WM short task gate later exposed a finite-sample defect of the
+estimate-then-average rule: each new `What` remains noisy even when `Q=W`, so
+an exponential tracker has a nonzero stationary error. Residual response
+mirroring (RRM) makes a substantive rule change. Given the same local probe
+and observed child response, it predicts the child response through Q and uses
+only the residual:
+
+```text
+u       = conv(z, W),
+uhat    = conv(z, Q),
+Delta Q = eta_M corr(z, u-uhat) / (count sigma^2).
+```
+
+In expectation this is the same contraction toward W, but when Q exactly
+matches W the update is zero for every individual probe rather than only in
+expectation. The readout uses the identical signed response residual. An
+executable audit measures fixed-point update RMS `2.75e-18`, response-residual
+fraction `3.08e-17`, and zero update dependence on forward parameters after
+the observations are fixed. RRM needs one extra local Q prediction convolution
+per mirror event, which is charged separately. It remains inherited local
+weight estimation, not SDIL novelty.
+
 ## 2. What is sufficient for a descent step
 
 Flatten all forward parameters into `theta`, let `p = grad L(theta)`, and let