The Hamido Framework: Emergent Spacetime from Quantum Matter – Geometry Correlations

Abstract: We propose the Hamido Framework, a theoretical model in which spacetime is not fundamental but emerges from quantum correlations between matter and discrete geometry. The framework introduces a unified Hamiltonian encoding matter–geometry interactions, ensuring unitarity and Lorentz invariance. We derive effective Einstein-like equations in the semiclassical limit and show how entanglement entropy acts as the fundamental building block of spacetime. A toy model with qubit registers illustrates the emergence of effective distances from correlations. The framework predicts testable signatures in quantum simulations, black hole evaporation, and primordial imprints in the cosmic microwave background.