Introduction and proof boundary

Cheung's phased-pruning study introduces a task-gated multilayer perceptron with early density manipulation, subsequent magnitude pruning, cue diagnostics, and hidden-activation noise CheungPruning. The supplied implementation 067a_code_sub_v2.py and accompanying manuscript Combined 067A Num v3 (1).docx are the specific objects audited here CheungSupplied067A.

The mathematical question is not whether one can attach theorem labels to the reported numerical tables. It is which conclusions follow from explicitly stated assumptions, which require a checkpoint-specific certificate, and which are false for the architecture class.

Probabilistic pruning theory already provides approximation results under specified weight laws QianKlabjan. Recent one-shot magnitude-pruning analysis likewise uses explicitly restricted models Koyuncu. These works do not establish a universal task-cue threshold or a developmental trade-off for the trained 067A network. The lottery-ticket literature also distinguishes pruning, initialization, and subsequent optimization FrankleCarbin.

principal corrections. The following distinctions organize this paper.

1. Density is a connection-count control, not a sufficient statistic for cue use or noise sensitivity.

2. A magnitude mask is an orthogonal coordinate projection in parameter space. It is not generally an orthogonal projection of hidden representations.

3. Fixed masks commute. Fixed-weight nested magnitude pruning also has an exact nesting identity.

4. Learning between pruning operations can change rankings and therefore invalidate that identity.

5. Accuracy is a discontinuous decision functional. Lipschitz control of logits does not, without a margin assumption, give Lipschitz control of accuracy.

6. A smooth surrogate pruning surface is a changed mathematical object, not the finite hard-pruning surface.

7. An ambiguous cue has no intrinsically preferred task. Accuracy against visual labels measures visual-rule retention, not task-neutral ambiguity resolution.

of the results. All propositions and theorems below are proved either directly or by an explicitly identified standard concentration inequality. The affine-Gaussian phase diagram is an exactly solved comparison model. Its applicability to a saved ReLU network is conditional on a stated approximation certificate. The supplied numerical values are treated as reported observations, not independently reproduced results.