The Equation of Everything (SEoT): A 4D Elastic Unified Framework for Gravity, Matter, and Dark Energy

We introduce the “Equation of Everything” (SEoT), a unified framework based on 4D elastic extensions of spacetime. The SEoT formalism integrates gauge, fermionic, and gravitational sectors into a single elastic action, where deformations into hidden dimensions generate effective interactions observable in 3+1D. Projected onto a Friedmann–Lemaître–Robertson–Walker background, the elastic stress-energy yields a dynamical component that behaves as quintessence or Early Dark Energy (EDE), providing a geometric–elastic interpretation of Einstein’s equations. The framework connects cosmology with particle physics, offering predictions for entropy growth, threshold effects, and dimensional projections relevant to large-scale structure. This article constitutes the mathematical core for subsequent applications to the Hubble tension and black-hole elasticity scenarios.