Relational Realization Theory (RRT) I: A Pre-Geometric Operator-Algebraic Architecture for Quantum Foundations and Gravitational Vacuum Decoupling

Relational Realization Theory (RRT) is a pre-geometric, operator-algebraic framework in which spacetime and metric distance are treated as emergent operational outputs of an underlying quantum-relational substrate. The foundational description is an atemporal unital C^*-algebra equipped with a state functional (\mathfrak A, \omega). At the primitive level, RRT does not assume a continuous manifold, background metric, external temporal parameter, or predetermined tensor-product factorization. To prevent category errors between mathematical structure and physical assertion, the framework distinguishes four epistemic layers: ontological primitive, structural mathematics, RRT physical postulates, and empirical interface parameters. Within this architecture, algebraically admissible relational configurations are distinguished from the subset interpreted as physically realized. Representation-disjoint sectors are introduced as the mathematical basis for the RRT concept of \emph{Quantum Resting}. RRT postulates that emergent gravity couples only to the realized operational sector, so that representation-disjoint sectors have vanishing active stress-energy. A closed-circulation postulate provides a discrete conservation mechanism whose continuum correspondence remains an open derivational problem. At the macroscopic interface, we adopt trace-free Einstein field equations, which algebraically decouple uniform w = -1 condensates, mitigating the direct gravitational sourcing of Lorentz-invariant vacuum contributions within the trace-free field equation without truncating canonical commutation relations.