Theorem: Psy01-A release

For the objects and assumptions explicitly defined in this paper:

1. conflicting-task performance and cue influence obey Theorems thm:cueobstruction and thm:cuecertificate;

2. a universal low-density cue-loss threshold near twenty percent is excluded by Theorem thm:nothreshold;

3. Gaussian stress admits global and frozen-gate certificates with explicit errors;

4. identical density and identical clean outputs do not determine stress tolerance;

5. fixed-weight nested magnitude pruning equals one-shot pruning at the same final integer counts, while learning can change the late ranking;

6. logit and smooth-observable stability are quantitative, but accuracy stability needs a margin hypothesis and hard density control need not be continuous;

7. the declared affine-Gaussian comparison has a proved conditional, non-monotonic trade-off and an increasing maximizer curve;

8. transfer of that trade-off to a ReLU checkpoint requires the strict error inequalities of Theorem thm:transfer;

9. concentration statements require their stated independence, bounded-influence, or held-out-evaluation conditions.

No universal architecture-specific density threshold, unconditional pruning phase diagram, biological causal identification, or treatment conclusion is established.

Proof. Items (i)–(ix) are precisely the results proved in the cited sections. The counterexamples exclude strengthening them to the stated universal assertions. The biological identifications and intervention effects are not assumptions of any theorem and have not been supplied by an independent empirical correspondence.