Theorem: Psy04-B mathematical release

For the finite processes and hypotheses defined here:

1. scheduled ancestors upper-bound unconditioned operational influence, including with untouched references;

2. late-query freshness and cut completeness yield the stated classical and quantum factorizations;

3. the complete two-state classical cut satisfies the sharp average benchmark $3/4$;

4. the standard qubit code has a sequential local Enter representation and attains its sharp qubit value;

5. the specified depolarizing storage has the exact retention score and threshold;

6. complete neutral scoring, parameter stability, and complete-law allowances give the robust gap;

7. conditional fixed-sample and anytime rules exclude the declared classical null at their stated error levels;

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

9. neither scheduled ancestry, RAC success, nor carrier-only history dependence alone certifies quantum environmental memory.

The exclusion is conditional on capacity, causal access, freshness, and justified error allowances. It does not establish those hypotheses from the record alone.

Proof. Theorem thm:schedule establishes the support claim. Theorem thm:factor establishes the cut factorizations. Theorems thm:classical, thm:qubit, thm:qubitoptimal, and thm:retention establish the benchmarks and storage claim. Theorem thm:neutral, Theorem thm:completescore, Proposition prop:parameterstability, and Theorem thm:robust give the record and robustness claims. Theorems thm:test and thm:anytime give the statistical guarantees. Theorem thm:covering and Proposition prop:coveringupper give the finite-capacity claims.

Theorem thm:nonentailment, Proposition prop:environmentbound, and Example ex:causalbreak establish the environmental non-entailment boundaries. The cut and freshness counterexamples show why the remaining assumptions are not conclusions of success alone.