theory: prove estimator and innovation regimes

1 files changed, 18 insertions, 0 deletions

diff --git a/RESULTS.md b/RESULTS.md
index 0650f04..f7873a1 100644
--- a/RESULTS.md
+++ b/RESULTS.md
@@ -429,6 +429,23 @@ the frozen 90% d4 threshold; **no prefix is eligible and task seeds 6--8 remain
 teaching directions are often strongly aligned even in mediocre runs, pointing next to regression
 gain/tracking over the moving trajectory rather than simply adding vectorizer capacity.
 
+## Theory package and executable predictions
+
+`THEORY.md` proves the exact linearized variance of simultaneous Rademacher perturbation,
+including its cross-layer term; bounds centered finite-sigma bias; gives a smooth-loss descent
+condition that separates angle, gain, and curvature; proves the neutral-period innovation/SNR
+result and task-fit absorption failure; and tabulates query/work/memory assumptions across the
+main comparison set.
+
+The deterministic numerical verifier covers every frozen C5 axis. Across depth 2/4/8, width 8/32,
+and K1/4/16, empirical perturbation MSE is within 1% of the exact prediction in the reported cases.
+The finite-difference bias has log-log slope `2.000000` in sigma. A quadratic example changes from
+descent to ascent on opposite sides of the predicted learning-rate threshold. Neutral predictor
+residual power matches `(1-eta_P)^(2t)` across three rates and four update counts. Finally,
+neutral residualization raises the teaching squared cosine from `0.7492` to `0.9656`, whereas
+task-period fitting lowers it to `0.5395` by removing soma-correlated teaching. **The frozen C5
+theory package and numerical checks pass.**
+
 ## Paper-faithful non-backprop baselines
 
 `PETITE` in the initial request is treated as **PEPITA**. Implementations and hyperparameters were
@@ -496,6 +513,7 @@ canonical d2 comparison: `experiments/ep_depth2_sweep.sh`; near-parameter compar
 `experiments/ep_matched_sweep.sh`.
 C2 direct causal diagnosis: `experiments/c2_nodepert_validation.sh` followed by
 `python experiments/analyze_c2_nodepert_validation.py`.
+Theory checks: `python experiments/verify_theory.py`.
 Audited aggregate tables: `experiments/analyze_verified.py`. The claim-locked finalizer is
 `experiments/finalize_claims.sh`; it rejects missing/dirty inputs, regenerates both main figures,
 their captions, source-hash manifest, and `results/audited_tables.md`, then runs all smoke checks.