Abstract

We develop a proof framework for the three computational interventions implemented in the supplied 068a_antidep_modes_v2.py: gradient-ranked connection regrowth, noise-scheduled adaptation, and activation modulation. We prove that weight-displacement norms do not control the implemented function when biases, damping, activation choice, or parameterization are allowed to change. A budget vector separates these controls from structural changes and training cost. For the actual post-activation-noise architecture, we establish damped path bounds, margin-based stress certificates, coupled parameter comparisons, and conditional ranking criteria. A signed sparse-gradient repair has an explicit local descent guarantee; the code's magnitude-ranked random initialization does not inherit it. Exact-count and random-stream repairs address matching tolerance, support gaps, endpoint regrowth, stage labeling, and secondary pruning. A separately specified finite quantum stochastic network has an exact classical Markov boundary, complete measurement records, and reference-stable intervention bounds. Two-level examples give exact phase-sensitive classification, coherence-to-population conversion, and a robust calibrated contrast. Equal operational channel distance nevertheless does not imply equal performance. The classical simulation, the quantum extension, and their pharmacological analogies are not identified. No newly executed numerical ranking, quantum computational advantage, antidepressant mechanism, or clinical treatment recommendation is asserted.