The Lehto Emergent Gravity (LEG) Framework: A Discrete Causal Derivation of the Standard Model and General Relativity

This paper presents the Lehto Emergent Gravity (LEG) framework, a discrete 3+1D causal graph theory that derives both General Relativity and the Standard Model mass spectrum from first principles. By modeling spacetime as a Directed Acyclic Graph (DAG) governed by WENO-5 non-linear geometric reconstruction, we demonstrate that fermions emerge as discrete pi-phase topological step discontinuities. The analytical WENO-5 action of this defect establishes a rigid baseline for the electron mass. Furthermore, we prove that the generation scaling of the Muon and Tau perfectly maps to the Koide formula via discrete graph combinatorics. Finally, we establish local thermodynamic equilibrium within the WENO substrate to formally close the Jacobson (1995) derivation, proving that the Einstein Field Equations are an exact thermodynamic equation of state emerging from a stable, discrete causal network. Open problems regarding gauge corrections and specific lattice combinatorics are explicitly defined.