protocol: freeze dynamic projection training gate

1 files changed, 26 insertions, 0 deletions

diff --git a/THEORY.md b/THEORY.md
index f659d0f..b8416a3 100644
--- a/THEORY.md
+++ b/THEORY.md
@@ -571,6 +571,32 @@ transient loss and parameter growth. This is consistent with the two-sided
 condition above: sign control is necessary but does not bound the evolving
 gain `d c` or nonnormal deep-network transients.
 
+The post-S0 dynamic controller instead separates a slow neutral predictor from
+a fast instruction-off projection. On the current minibatch, let its neutral
+residual be `e0=a0-P h-b`. Each cell forms
+
+```text
+q_t = Cov_t(e0, h) / Var_t(h),
+e_perp = (e0 - mean_t(e0)) - q_t (h - mean_t(h)).
+```
+
+Only `s+e_perp` enters plasticity. The fit for `q_t` never observes `s`, so it
+cannot regress away a task instruction merely because that instruction is
+correlated with soma. For the diagonal affine traffic intervention,
+`e0=D h+c` and hence `e_perp=0` in exact arithmetic at every task state. The
+effective homogeneous coefficient is then `k=-lambda`, which satisfies both
+Jury bounds for the frozen positive learning rate, momentum below one, and
+small positive decay. Unlike a fixed negative margin, nulling `D` is invariant
+to changes in the nonnegative input-covariance eigenvalue `c`.
+
+This is an empirical local certificate for the intervention being tested, not
+a global stability theorem for a nonlinear ResNet. Finite-batch regression,
+roundoff, cross-layer nonnormality, and traffic outside the diagonal affine
+family remain possible failure modes. The separately frozen D1 training-prefix
+gate in `DYNAMIC_INNOVATION.md` therefore requires both the measured local
+certificate and bounded loss, parameter, optimizer, and BatchNorm trajectories
+before any validation endpoint can open.
+
 ### Intermittent feedback tracking can hide behind a final cosine
 
 An idealized mirror event every `k` task updates uses