The Repair Saturates the Gate: Context Noise as a Degeneracy Diagnostic in Active-Dendrite Continual Learning

Active-dendrite continual-learning systems condition each neuron's plasticity and routing on a task-context signal. A companion audit (S1) found that such networks never develop segment-task specialization and that a constant bias b on the own-segment dendritic input causally repairs the learning term (d_ell up to +4.6). Every result in that line - including the repair itself - was obtained under oracle context. We ask the question the line left open: when the context signal is wrong, what survives? Under the worst-case evaluation protocol (each sample's context one-hot flipped to a uniformly random other task with probability rho), the answer is: everything, at every noise level tested. Final accuracy moves by at most 0.25 points at rho <= 0.4 for the base system and by at most 0.01 points for the repaired one; the repair's paired gain (+4.80, t=17.0, on MNIST) is retained at 100-105% under noise on MNIST and 100-124% on Fashion-MNIST. Zero noise sensitivity is not robustness - it is a symptom. Mechanism probes show why: the trained dendritic gate is context-degenerate. Its value under the correct context and under every wrong context is identical to four decimals (0.565); after the repair (b=10) context swaps change at most 0.02% of predictions on average (worst pair 0.15%); and the dendritic weight columns stay mutually orthogonal (cosine ~0.003) throughout training. Two degenerate controls then locate what the repair actually repairs. A constant-gate control that pins the gate at its measured baseline value (0.565) reproduces the base network, not the repair - merely holding the gate constant buys nothing, because the base system already runs at that constant. A no-gate control (h = kwta(t), same trunk, same anchor chain) recovers most of the repair's benefit on MNIST (67.50 vs 68.67, -1.16, t=-2.7) and numerically exceeds it on Fashion-MNIST (44.27 vs 42.89): the repair functions as a saturating soft deletion of the gate (sigma(10+u) ~ 1), and what it buys is the removal of a constant ~0.57 damping factor - not restored routing. A 2026-10-27 audit corrected two harness defects (an unenforced lambda, a width-mismatched control); all experiments were re-run and the first version's MNIST gate-removal equivalence is retracted; both versions of the records are retained. Files: main.pdf (full paper), LaTeX source (main.tex/main.bbl/refs.bib), the preregistration, its data-closure report, and the 2026-10-27 amendment (prereg/), the four experiment scripts (code/), and the raw per-seed records including superseded versions with a deprecation notice (results/). Companion code and all records: https://github.com/zhouranxi/delp-anchor-budget . Related records: precursor https://doi.org/10.5281/zenodo.23602281 ; S1 (the repair explained here) https://doi.org/10.5281/zenodo.23637973 . This record is a timestamped preprint deposited to establish a citable public record independently of journal acceptance.