Relational Quantum Gravity in a Self-Consistent Einstein–Scalar Sector

The first seven papers construct one Schwarzschild Einstein–real-scalar quantum sector through operator selection, native quantum dynamics, local stress, nonlinear Einstein response, Palatini BV/BRST structure, and regulated quantum-master analysis. Paper VII leaves a nonzero restricted physical sector after an explicit global QME-descent obstruction. Paper VIII asks how physical quantum identity and gravitational visibility relate once that surviving sector is given an exact nonlinear Einstein realization.

The realized state space carries a physical-owner projection, a state-dependent stress source, and a smooth Lorentz metric satisfying the exact nonlinear Einstein equation. The gravitational response is classical and nonlinear; the quantum structure resides in the state, physical-owner, BV/BRST/cohomological, and source sectors. In this paper, relational quantum gravity denotes the relation among quantum physical ownership, quantum-state-dependent source, exact nonlinear gravitational response, and their quotient structures.

The physical-owner and gravity-visible equivalence relations are globally incomparable. Anchor continuation preserves physical ownership while changing realized source and geometry. Conversely, coherent phase pairs supply distinct physical owners within a single gravity-visible source class, and a matched finite-number/coherent construction gives the same nonseparation across qualitatively different quantum states.

On the fixed nonlinear branch family, complete scalar-curvature and curvature-gradient image data give an intrinsic rigidity theorem. Equality of the joint invariant images recovers the source parameter. After local Lorentz-frame descent, this source classification is equivalent to the represented physical smooth-diffeomorphism classification of the metric family.

The completed-Fock analysis also yields a sharp functional boundary. Normalized number states have a positive source component growing linearly with occupation, excluding a global norm-bounded completed-Fock stress extension agreeing with every number source. An infinite-support coherent family lies in an explicit stress domain, while every positive finite occupation has an exact conserved nonlinear Einstein realization.

The resulting theorem package separates physical quantum identity from gravitational visibility and characterizes their realized relation at the stated scope. It does not independently quantize metric degrees of freedom: the metric response remains a smooth classical Lorentz geometry sourced by quantum-state-dependent matter, while quantum geometry in the stronger sense remains a later mathematical layer.