Relational Algebraic Quantum Spacetime (RAQS): A UV-Complete Background-Independent Framework with Forced Emergent Limits in Gravity, Cosmology, and Gauge Theory

Relational Algebraic Quantum Spacetime (RAQS) is constructed as a non-perturbative, background-independent quantum framework defined by a directed net of finite dimensional matrix algebras indexed by causal diamonds, equipped with overlap consistent quantum channels and a microscopic area dimension scaling law. The theory is formulated entirely in finite operator algebraic terms and does not assume a background spacetime manifold. Within this structure, global ultraviolet complete evolution follows from finite-dimensional consistency and overlap-preserving channel gluing. The Einstein field equation is derived from stationarity of a generalized entropy functional in which the Bekenstein Hawking area term arises directly from the microscopic dimension law rather than from black hole thermodynamics. Linearization of the emergent Einstein Hilbert action yields the standard massless spin propagator and tree level graviton amplitudes. In the cosmological sector, the Mukhanov Sasaki equation and the standard scalar and tensor power spectra arise from the quadratic relative-entropy structure of the finite state space. The framework predicts a structurally unavoidable finite-patch infrared decoherence correction to primordial power spectra that is exponentially suppressed by total patch entropy and cannot be reproduced by any local effective field theory counterterm. In asymptotically AdS sectors, algebraic reconstruction yields exact bulk boundary correlator matching under explicitly stated conditions. Using Doplicher Roberts reconstruction combined with a globalizability condition that identifies gauge anomalies with topological gluing obstructions, the minimal connected compact gauge group compatible with observed sector data is uniquely SU(3) × SU(2) × U(1), and the anomaly-free minimal chiral matter content per generation is recovered. All assumptions are explicitly stated as axioms or observational premises. The scope of each derivation is clearly delimited. The framework is ultraviolet finite at every scale and relocates the Bekenstein Hawking area law from thermodynamic postulate to microscopic algebraic input.