Quantum Geometric Framework (QGF)

https://zenodo.org/records/15424808

The Quantum Geometric Framework (QGF) is a categorical theory wherein spacetime, gravity, and matter emerge from the entanglement structure of quantum states, without assuming a classical background manifold. It reconstructs geometry from modular tensor categories and informational flow, replacing metric structure with a topological and algebraic foundation.

This v2.0 release presents a foundational rederivation and formal expansion of the framework. It includes a complete formulation of entanglement-induced Lorentzian geometry using mutual information and modular flow, as well as a derivation of gravitational dynamics via entropic constraints. The Einstein field equations are recovered from modular Hamiltonians defined over tensor networks.

Matter fields and gauge interactions arise from fusion and braiding rules in modular tensor categories. The Standard Model is constructed categorically by combining color, electroweak, and charge sectors into a unified algebraic object class. A Grand Unified embedding is supported through modular condensation and fusion bracket convergence, showing explicit recovery of classical Lie algebra structure in the large-level limit.

This version also introduces full simulation support, including verification of constraint algebra closure over large entanglement graphs, entropic renormalization group flow to continuum correlators, and calibration of bond dimension and modular time to physical observables. The framework yields testable predictions for cosmological observables such as the scalar spectral tilt and tensor ratio, rare lepton-flavor-violating Higgs decays, and primordial black hole mass spectra.

The archive includes all LaTeX source files, modular category data (in CSV format), simulation notebooks, and code under an MIT License, enabling full reproducibility and open development.