Abstract

Phased pruning simulations suggest that late connection removal can alter resistance to cue interference and vulnerability to internal noise. Turning these observations into mathematics requires distinguishing statements about a particular trained network from universal statements about an architecture class. We provide a self-contained analytic framework for the task-gated ReLU architecture used in the 067A model. We prove cue-utilization bounds, an indistinguishability obstruction for conflicting tasks, parameter perturbation estimates, Gaussian stress certificates, exact identities for nested magnitude pruning, and conditional concentration bounds. An explicit sparse construction disproves a universal cue-loss threshold near twenty percent density. Fixed-weight nested pruning is shown to agree with one-shot pruning at the same integer retention counts; schedule dependence instead requires learning, re-ranking, or a change of allocation rule. Hard finite-width pruning does not generally define a Lipschitz density surface. A differentiable relaxation and an exactly solved affine-Gaussian comparison model provide valid replacements, including a conditional, non-monotonic selectivity–fragility trade-off and an increasing maximizing curve. We also establish that identical masks and identical clean outputs need not determine identical stress tolerance. Cheung's landmark manuscripts inform the separation of construction, fluctuation, observation, and causal claims, but their quantum results are not identified with neural-network theorems. A source-code audit supplies exact-count pruning and random-stream repairs. No empirical density threshold, biological pruning mechanism, or treatment recommendation is asserted as a mathematical consequence.