Relational Algebraic Quantum Spacetime (RAQS): Framework, Consistency Proofs, Gauge Structure Derivation, and Beyond-EFT Cosmological Prediction

This Zenodo deposit contains a set of four linked research papers establishing the framework of Relational Algebraic Quantum Spacetime (RAQS) and several structural consequences derived within it. The works collectively present a background-independent formulation of quantum spacetime in which geometry, gravitational dynamics, cosmological perturbations, and gauge structure emerge from a relational algebraic foundation. RAQS models spacetime as a directed net of finite dimensional operator algebras indexed by causal diamonds, together with overlap consistent quantum channels governing relational dynamics. The framework is mathematically finite at every scale and therefore avoids ultraviolet divergences by construction. A microscopic dimension area scaling law links the algebraic structure to spacetime geometry, providing the informational origin of the Bekenstein–Hawking entropy relation. Within this structure, several results are derived. First, the Einstein field equation is obtained from stationarity of a generalized entropy functional defined on the causal-diamond algebra. In this derivation the Bekenstein Hawking area term arises from the finite Hilbert space dimension law rather than being postulated from black-hole thermodynamics. Linearization of the resulting effective action reproduces the standard massless spin 2 graviton sector and the tree level gravitational amplitudes of classical general relativity. Second, cosmological perturbation spectra arise from the quadratic relativ -entropy geometry of the finite state space. In the semiclassical limit this yields the Mukhanov Sasaki equation and the standard scalar and tensor power spectra associated with inflationary cosmology. Third, the framework introduces a globalizability constraint for charged sectors on the causal diamond net. This constraint identifies gauge anomalies with topological obstructions to consistent sector transport across overlapping diamonds. When combined with Doplicher Roberts reconstruction and minimality principles, this forcing mechanism yields the Standard Model gauge groupSU(3) × SU(2) × U(1) as the minimal connected compact gauge group compatible with observed charge structure. Fourth, the finite dimensionality of causal-patch Hilbert spaces produces a structurally determined prediction beyond effective field theory. A universal infrared correction to cosmological power spectra arises from the finite information capacity of causal patches, generating an exponentially suppressed decoherence correction that cannot be reproduced by any local EFT counterterm. The present deposit includes four papers that together establish the RAQS framework and its principal consequences. The first paper introduces the full RAQS construction and derives the Einstein equation, graviton sector, cosmological perturbation spectra, AdS correlator reconstruction conditions, and the Standard Model gauge group. The second paper proves the non-circularity of the Einstein equation derivation, demonstrating that the Bekenstein Hawking entropy relation used in the argument follows from the RAQS microscopic dimension law rather than from assumptions about the Einstein equation itself. The third paper develops the anomaly obstruction correspondence, showing that gauge anomalies correspond to Čech-cohomology obstruction classes preventing globally consistent sector transport on the causal diamond net. Under observational sector constraints and minimality, this structure forces the Standard Model gauge group. The fourth paper derives a structurally determined beyond-EFT cosmological prediction, identifying a universal infrared decoherence correction to primordial power spectra determined by the finite entropy of cosmological causal patches. Together these works present a mathematically finite and background independent approach to quantum spacetime in which geometry, gravitational dynamics, cosmology, and gauge structure arise from a unified relational algebraic structure.