Theorem: Em06-A analytical release

For the fixed data printed in this manuscript:

1. the classical functional (eq:observable), its dependence support, and its plateau gauge domain are defined and proved;

2. its scalar-only compact-test representation (eq:q)–(eq:representation) is exact;

3. the quantum representative, its self-adjoint domain, and the positive normalized state family are constructed;

4. the mean and variance acceptance conditions are proved separately by (eq:mean) and (eq:variance);

5. spectral convergence holds in $W_2$, with the exact rate (eq:W2) and fixed-support uniformity;

6. a nonzero classical target and the preparation-response diagnostic are evaluated by (eq:witness) and (eq:diagnostic).

The outcome is a repaired scalar-only limit for the first plateau relational coefficient.

No quantized metric insertion, full nonlinear relational limit, interacting gravitational product, unrestricted gauge theorem, Einstein dynamics, metric reconstruction, or holographic map is released. The XI-G class obstruction is untouched. No inherited quantum-response coefficient is admitted; XVI-N's separate Route B is not discharged; O.1 is not closed; H2, I3, and J2 are not resolved by this manuscript; XV-B is not opened.

Proof. Propositions prop:plateau and prop:support prove (i). Propositions prop:test and prop:testgauge prove (ii). Lemma lem:domains and the explicit vector construction (eq:states) prove (iii). Theorem thm:main proves (iv) and (v). Proposition prop:witness and Theorem thm:diagnostic prove (vi).

The maps in the proof retain a classical metric parameter and a free scalar carrier throughout. Proposition prop:noadmission establishes the non-transfer to the frozen cubic admission problem. No map or dynamical object needed for any of the excluded claims is constructed. Those claims are therefore not additional parts of this release.