mechanism: separate BCI role from performance velocity

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@@ -632,6 +632,59 @@ the loss-producing part of training. Endpoint alignment must be reported with
 the alignment trajectory and task loss. This is a standard tracking fact used
 to audit the mirror baseline, not an SDIL novelty claim.
 
+### Why instantaneous gradient feedback cannot reproduce the BCI derivative sign
+
+The failed oral-B model calibrated its apical vectorizer to the instantaneous
+negative loss gradient. Let `e_t>0` be the target-minus-cursor error during an
+active trial and let `s_i` be the signed causal role of cell `i` (`s_i>0` for
+P+, `s_i<0` for P-). With squared loss, the perfect calibration target is
+
+```text
+r_i(t) = e_t s_i.
+```
+
+Consequently the P+ minus P- residual contrast is a positive constant times
+`e_t`. Whenever current error is smaller in error-reduction epochs than in
+error-increase epochs, the Harnett separability statistic
+
+```text
+0.5 * [E(P+ - P- | error decreases)
+       - E(P+ - P- | error increases)]
+```
+
+is negative. Adding error velocity as an input feature does not fix this:
+regression against `e_t s_i` still assigns the causal coefficient to error
+magnitude and has no reason to assign it to velocity. The complete negative
+36-run screen is therefore a structural falsification of that target, not a
+learning-rate failure.
+
+A derivative-faithful candidate separates causal-role identification from the
+temporal performance modulator. With Rademacher perturbations `xi`, observe
+only the scalar cursor under antithetic state interventions:
+
+```text
+z+ = s^T (h + sigma xi),       z- = s^T (h - sigma xi),
+q_i = ((z+ - z-) / (2 sigma)) xi_i.
+```
+
+Then `E[q_i]=s_i`; no task loss, gradient, transpose weight, or reverse graph
+is used. Define the within-episode performance innovation
+
+```text
+delta_t = |e_(t-1)| - |e_t|,
+r_i(t) = delta_t * m_i,        m_i approximately s_i.
+```
+
+Now the same separability statistic is positive by construction when both
+improving and worsening epochs occur. More importantly, this is not merely a
+metric relabelling: `delta_t` is the scalar outcome that modulates the local
+eligibility update, while sparse causal perturbations amortize the
+neuron-specific role vector `m`. Whether that three-factor temporal rule
+actually learns, preserves residual decorrelation, and survives a plasticity
+lesion remains an empirical gate. Direct online control is not implied; in
+fact applying `r` as an immediate state correction would reinforce both good
+and bad velocity signs and is therefore excluded from the first recovery.
+
 ## 4. Hardware-independent complexity
 
 Let `H` be the number of hidden layers, `K` the perturbation directions per
@@ -675,4 +728,6 @@ quadratic finite-sigma bias law; the smooth-descent step threshold; the
 conditional-projection Pythagorean identity and norm-matching direction
 invariance; neutral predictor convergence across `eta_P` and update counts;
 the multiplicative residual-coupling operator and its unstable positive mode;
-and the task-fit teaching-signal absorption predicted above.
+the task-fit teaching-signal absorption predicted above; and the BCI
+instantaneous-gradient sign conflict versus the temporal-difference role
+factorization.