Theorem: Quantum-certificate nontransfer and non-determination

On the explicit comparison domains defined in this paper, the following implications are invalid without additional hypotheses:

1. classical field equations, causal commutator data, and a prescribed wavefront condition imply a selected positive state or a completed composite contraction;

2. pure-trace or finitely many kernel evaluations imply a unique full kernel, its free-shell functional, or its microlocal admission;

3. late source equality implies equality of retarded responses;

4. finite-probe cancellation, image-closure membership, or a projected identity implies exact repair in the actual counterterm class;

5. a positive formal quantum correction cancels a fixed nonzero classical coefficient;

6. free gauge closure implies interacting closure;

7. identical classical record laws or exact subdivision of one finite channel determines complete residual instruments or a unique continuous-time evolution.

Exact affine repair is instead the condition $[D]=0$ in ${\mathcal{V}}_{\mathrm{def}}/\mathrm{im}B$. A defined identity transports by the matching equations of Lemma lem:transport; no such map is furnished between the native clocks or by the reported external benchmarks.

These conclusions are separation results, not universal nonexistence theorems for the native quantum targets.

Proof. For (i), Proposition prop:state gives both covariance nonuniqueness and a failure of positivity with unchanged algebraic and singularity data. Proposition prop:product shows why separate factor definitions do not give a raw product.

For (ii), Propositions prop:trace and prop:microcausal, together with Lemma lem:finite-tests, give explicit blind sectors.

Proposition prop:memory proves (iii). Propositions prop:repair, prop:dense-image, and prop:projection prove (iv). Lemma lem:formal proves (v). Proposition prop:free-interacting proves (vi). Proposition prop:record and Proposition prop:evolution prove (vii).

The exact repair criterion and conditional transport statement are proved in Proposition prop:repair and Lemma lem:transport. No predecessor quantum calculation is used in these proofs.