Abstract

We develop a source-aligned proof framework for recurrent classification and a computational probe battery in the supplied 068g_cognitive_impact_v2.py. The ordinary and biased evaluators inject noise through different interfaces and are not unrollings of the earlier feed-forward stress model. Using the actual PyTorch GRU convention, we prove an ordinary-ReLU invariant cube despite unbounded input noise, bounded states for either externally tanh-activated path, and a finite-horizon envelope for biased ReLU trajectories. Gate-aware Lipschitz constants, exact cell Jacobians, parameter residuals, and temporal propagation give conditional perturbation and margin certificates. Repeated static inputs preserve the original task information; independent per-step corruption changes the observation law but does not create independent latent examples. We derive exact Gaussian-task Bayes references and a noiseless blend reference whose information loss is non-monotonic in distractor weight. Invertible rotation and scaling preserve ideal label information, whereas the implemented blend ignores the conflicting labels. Simultaneous and history-conditional battery certificates separate probe accuracy, clean-to-probe gaps, checkpoint changes, and scar-attributable intervention effects. An updated static audit distinguishes persistent defects from controls now used by the source, including the 131-candidate per-seed sweep and three-seed iso-displacement routine. A separately declared finite input-driven quantum model supplies fixed-sector forgetting bounds, a persistent-register obstruction to global forgetting, and an exactly solved delayed phase-label pilot. No executed probe ranking, validated cognitive construct, biological treatment mechanism, quantum computational advantage, or inherited field-theoretic admission is asserted.