Theorem: Psy03-D mathematical release

For the objects and hypotheses printed here:

1. the uncued rule process is unobservable from the point history, and its exact population classification optimum is $3/4$;

2. two rule IDs implement the same function, and the stated switch and disagreement frequencies hold;

3. explicit, delayed, erased-cue, and feedback protocols have the stated information references;

4. old-function responses, repeated errors, entropy, flexibility, and recovery patterns have distinct operational meanings;

5. sequence-level mean, ratio, paired, and censored-pattern certificates hold under their freshness and denominator hypotheses;

6. the masked-gradient and reference-preservation identities hold;

7. per-tensor multiplier cancellation and reversed global-score protection have the stated counterexamples;

8. executed matching, conditional interpolation, and isoacute calibration have the stated certificates;

9. a rule-independent quantum processor inherits the uncued obstruction, while the separately cued pilot has the exact retention and execution formulas.

Adaptation requires observable evidence of change. Response repetition alone does not identify rule perseveration.

No executed ranking, validated cognitive construct, biological treatment mechanism, clinical recommendation, quantum advantage, or inherited analytic admission is established.

Proof. The preceding independent proofs establish each positive statement. Their hypotheses exclude the unsupported observation, optimization, matching, and interpretive transfers. The absent biological correspondence is not a premise of any theorem.