Discussion and mathematical release

The recurrent upgrade changes the perturbation interface, not only the network depth. Its ordinary ReLU states remain in a unit cube despite Gaussian input stress. Its biased ReLU states need a different envelope. Gate-aware constants and comparison tubes, rather than density or a gate-block spectral radius alone, determine the available stability certificate.

The probe battery mixes invertible shifts, reduced class separation, increased input uncertainty, altered recurrent perturbations, and coordinate interference. Each has a different task reference. The noiseless blend is especially diagnostic: a larger distractor coefficient can preserve all label information, even when a classifier trained on ordinary quadrants fails.

A legitimate structural-effect claim compares admitted intervention branches at common observation laws. A legitimate population certificate separates controller data from fresh assessment. A legitimate cognitive interpretation requires evidence outside these computation definitions.