Question, contribution, and proof boundary

The central question is:

Under what declared intervention budgets do structural repair, noise adaptation, and dynamical modulation improve a specified computational outcome, and when does a separately supplied coherence resource change the comparison?

Cheung's computational comparison supplies the direct motivation CheungModes. The earlier pruning study and pruning-cliff preprint concern related computational models CheungPruning,CheungCliff. The exact object audited here is the source supplied as 068a_antidep_modes_v2.py, not an unexamined repository revision Cheung068Code.

The paper has two tracks.

1. Classical track. We formalize the supplied feed-forward computation, prove conditional performance certificates and counterexamples, and repair the comparison protocol.

2. Quantum track. We independently define a finite open-system network, prove its classical boundary, and construct phase-sensitive records. It is an extension by mathematical analogy, not a reinterpretation of the Python simulation as quantum.

Psy01-A motivates the separation of masks, parameter geometry, margins, stress, and training schedules CheungPsy01A. Psy02-A motivates the separation of channels, coherence, instruments, and accessible records CheungPsy02A. Psy02-B supplies the corresponding complete-process and calibrated comparison architecture CheungPsy02B. Their roles are source records and methodological precedents. The independent statements used here have their hypotheses and proofs printed below.

names of the interventions. In theorem statements we use:

The source's “ketamine-like,” “SSRI-like,” and “neurosteroid-like” labels are retained only as declared biological analogies. They do not establish pharmacological correspondence.

boundary. The Lipschitz, concentration, and channel tools are standard. The contribution is their source-aligned application, the budget-insufficiency and ranking counterexamples, the exact small quantum comparisons, and the repaired evidential protocol. No theorem characterizes the convergence of the source's Adam training runs.

boundary. The source audit is static. No performance table is generated or independently reproduced here. The appended repair core is not reported as executed. The mathematical release does not depend on a passing script, successful compilation, or laboratory realization.