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

This eighth paper in the Schwarzschild Quantum Gravity series develops the relational quantum-gravitational structure of the self-consistent Einstein–real-scalar sector established in Papers I–VII. The quantum structure is carried by the matter state, physical-owner, BV/BRST, and restricted-cohomological sectors; the gravitational response is a smooth Lorentzian metric satisfying the exact nonlinear Einstein equation for the corresponding quantum-state-dependent stress tensor. The central result is that physical-state identity and gravitational visibility define distinct equivalence relations on the realized state space. Explicit constructions prove both failures of global factorization: a single physical owner can participate in distinct gravity-visible classes, and distinct physical owners can determine the same gravity-visible class. The latter phenomenon is realized both by coherent-state phase data and by matched finite-number/coherent states with identical gravitational source and geometry. The paper then identifies the domain in which gravitational classification becomes rigid. For the nonlinear realized family with fixed horizon and anchor data (h,a), the complete unparameterized joint image of scalar curvature and curvature-gradient norm determines the source parameter S. The proof first recovers a dimensionless shape parameter, exposes an exact involutive source duality, and eliminates the nontrivial dual through the intrinsic midpoint signature and logarithmic transport quadrature. Consequently, equality of the intrinsic joint image implies equality of source strength, and the gravity-visible quotient is equivalent to the represented physical smooth-diffeomorphism quotient on this family. Additional results establish regulator-independent physical ownership at the level of underlying state types, exact nonlinear Einstein realizations for every positive finite occupation, nontrivial gravity fibers, genuine quantum clock evolution with Bogoliubov mixing at fixed gravitational source, and a completed-Fock boundary: normalized number-state stresses admit no single globally norm-bounded extension, while explicitly constructed infinite-support coherent states remain within a proved stress domain. The resulting framework packages state, physical ownership, source, geometry, and their quotient relations into a matter-parametric relational structure, instantiated here by the Einstein–real-scalar model. The manuscript is accompanied by machine-checked Lean formalization, theorem and scope concordances, negative-result certification, and an explicit axiom audit.