Hierarchical Self-Referential Reconstruction Cosmology H: Categorical Foundations of a Unified Formulation of Quantum Gravity

This paper proposes and develops a unified framework for quantum gravitybased on information-theoretic primitives—the Hierarchical Emergent Framework(HSF). Grounded in the fundamental operational principles of “information distinguishability” and “finite-step describability,” this framework constructs a stratifiedmathematical category (the HSF category) through the dynamics of “self-referentialreconstruction.” We rigorously demonstrate that three prominent research programs in contemporary quantum gravity—the “It from Qubit” paradigm basedon quantum entanglement, causal set theory based on discrete causal orders, andthe ER=EPR conjecture asserting the duality of geometry and entanglement—caneach be formulated as specific representations of the HSF category under particular constraints. Furthermore, by constructing three category equivalence functors,we establish their mathematical isomorphism. This isomorphism stems from theirshared underlying logic based on information and self-reference. As direct corollaries of the unified framework, we derive a series of precise and testable cosmologicalpredictions, including characteristic values for CMB non-Gaussianity, distortionsin the primordial gravitational wave spectrum, a quantitative explanation for theHubble constant tension, and a slight evolution of the dark energy equation ofstate. This work provides a principled, mathematically rigorous unified foundationfor reconciling the diverse paths in quantum gravity research.