Topos-hypergraphs quantum geometry: an information-theoretic approach to emergent spacetime

This work presents a discrete quantum geometry where spacetime is a topos-hypergraph. From information principles, we derive the Standard Model's gauge group and parameters without fine-tuning, yielding unique, falsifiable predictions for gravitational waves and the CMB.The paper provides a complete and self-contained presentation of the theory. In Section II, we construct the informational site. In Section III, we detail the unified discrete action. Section IV explains the RG flow and the emergence of classical spacetime. Section V demonstrates how this framework naturally accommodates fermionic matter and derives the structure of the Standard Model from hypergraph topology. Finally, in Section VI, we present several precise, falsifiable predictions for cosmological observables that can be tested with current and near-future experiments.