Theorem: Psy04-A mathematical release

For the objects and hypotheses printed here:

1. the stochastic classical alternative reduces to mixtures of deterministic encoding-decoding tables;

2. every complete two-state classical memory satisfies the sharp average bound $3/4$;

3. the standard qubit code has an explicit sequential realization and attains the sharp qubit benchmark $1/2+1/(2\sqrt{2})$;

4. depolarizing storage has the exact retention score and threshold in Theorem thm:delay;

5. neutral attempted-run scoring preserves the classical bound and has the stated independent-loss quantum formula;

6. complete-law and channel allowances give the robust gap and implementation ledger;

7. fixed-sample and anytime tests have their stated uniform Type-I guarantees under fresh-run bottlenecks;

8. finite classical capacity has the stated covering formulation and upper certificates;

9. the benchmark does not entail quantum non-Markovianity or quantum environmental memory.

A statistically adjusted record can reject every model in the declared bounded classical-memory class. That conclusion remains conditional on its complete capacity, access, freshness, and discrepancy assumptions.

No experimental violation, biological memory identification, clinical conclusion, asymptotic computational advantage, spacetime emergence, or inherited analytic admission is established.

Proof. The preceding proofs establish each positive assertion. Propositions prop:loopholes and prop:largernull, Theorem thm:nonentailment, and Example ex:classicalmemory establish the relevant non-entailment boundaries. The experimental and physical correspondences are not hypotheses discharged by a mathematical score calculation.