The quadratic normalization

For the frozen instance and supported interfaces stated in this paper:

1. XI-A's signed action, quadratic operator, Euler coefficients, Noether split, and invariant tensor-density covariance have the retained local-chart interpretation;

2. the fixed-input completion jet ${\mathcal{J}}_g({\varphi }_m)$ is empty, while the vacuum fiber is nonempty;

3. the detector (eq:bump) has the same nonzero value after supported chart transfer whenever its support fits $D_{\ast }$;

4. the complete destructive report instrument retains the actual unmeasured residual and arbitrary untouched references;

5. the common-interface rational probability table obeys (eq:tablebound), and the finite-probe limitations of Propositions prop:coverage and prop:invisible remain explicit;

6. no operation reconstructs or sources the host, and no additional quantum-gravitational gate is passed.

Proof. Lemma lem:transfer and the supported restatements in Sections sec:action and sec:noether give (i). Restatement rest:empty gives (ii). Proposition prop:localdetector gives (iii). Theorem thm:instrument gives (iv). Theorem thm:table and Section sec:coverage give (v). Proposition prop:fixedhost, the declared analytical domain, and the absence of any quantum product or metric-update construction give (vi).

specification of the retained gravitational coefficients

This appendix records XI-A's finite coefficient prescription for (eq:Hdefinition); it does not select or calculate a graph CheungXIA.