Question, scope, and source discipline

The question is:

Under which explicit preparation and input-control assumptions do families of scalar-only plateau relational coefficients concentrate on their named classical values, and what survives at the normalized fluctuation scale?

The observable is the first relational coefficient, not a full finite-coupling nonlinear observable. Its architecture agrees with the first-order plateau construction described in Cheung's VII-A thm:first CheungVIIA and with the supplied Em06-A draft Em06A. Every identity needed here is rederived in the conventions printed below. No second-order theorem is imported.

The coherent-state mechanism is established mathematics Glauber,Hepp. Our contribution is the explicit quantitative package for this named scalar-only coefficient: compact-test estimates, finite families, residual-state assumptions, input control, and the separation between concentration and quantum fluctuations. We do not claim a new general coherent-state or semiclassical-limit principle.

The Wigner-measure literature provides a broader bosonic framework ANphase,ANgeneral. Its nonlinear propagation results have their own hypotheses ANpropagation. They are not premises of the fixed-input estimates proved here. Likewise, dynamical fluctuation theorems such as BenArous are comparisons, not substitutes for our exact displacement calculation.

precise weakening is retained. Only the scalar is quantized. The metric coefficient is fixed before the compact scalar test is passed to the quantum representation. We do not construct a quantized metric-dependent insertion, an interacting BRST/BV complex, or an interacting relational product. This retains the distinction emphasized in V and in the sharp joint insertion problem of VII-B CheungV,CheungVIIB.

attached XVII-A is a different project. The supplied file XVII-A.tex declares a finite-matrix ${\mathrm{AdS}}_2$ boundary reconstruction benchmark XVIIA. Its geometry, matrices, boundary algebra, and correspondence $U$ are not inputs here. No identification between its effect and the present Minkowski relational coefficient is asserted.

comparisons are not verified premises. Cheung citations refer to the supplied versions and excerpts. The added descriptions of VII-I and VII-J include theorem labels without the full corresponding proofs. We therefore use those descriptions only as comparison material Dossier, not as independently audited theorems or premises. In particular, a summary calling a landmark “verified” does not verify its signs, domains, or compatibility with the present model.