Quantum Informational Relativity: Foundational Structure, Microphysical Dynamics, Cosmological Predictions, and Numerical Validation (Complete Derivations and Unified Theoretical Framework)

Quantum Informational Relativity (QIR) proposes a unified formalism in which microphysical dynamics, spacetime structure, and cosmological evolution are consistently derived from an underlying informational field-theoretic framework. This monograph consolidates the complete formulation of QIR from the operator-level action and classical limit to the Hamiltonian structure, consistency relations, and effective constants and organizes it into a coherent, self-contained theory. At the microscopic level, QIR predicts informational solitons, canonical fluctuation modes, confinement, mass generation, and small but measurable shifts in Standard Model observables. A Wilsonian mapping links these scales to cosmology, producing a smooth continuation across 30+ orders of magnitude. Cosmologically, QIR generates percent-level deviations in the growth function and lensing potential, easing the S8 tension while leaving background distances unchanged. Fully nonlinear N-body simulations performed with a modified SWIFT engine confirm these signatures and reproduce realistic cosmic structures. Altogether, this work provides the first complete exposition of QIR as a mathematically consistent, observationally testable, and scale-continuous alternative to standard microphysical and gravitational dynamics.