The Entanglement Lattice Substrate and Emergent Spacetime

We present the complete foundational mathematics of EGESB-G2 Level 1. From the weighted entanglement lattice B=(V,E,W) with N~10^180 nodes and no background spacetime, we derive: the bulk Lagrangian and Euler-Lagrange equations; the Wheeler-DeWitt ground state W=e^-1; the Ryu-Takayanagi formula via max-flow min-cut; the continuum metric from spectral coarse-graining of the graph Laplacian; the Einstein equations via the Jacobson thermodynamic route; the effective cosmological constant as vacuum entanglement tension; the modified Friedmann equation with w0=-0.97, wa=-0.14; emergent time from entropy monotonicity and the Page-Wootters connection. Each derivation is self-contained. Open problems are identified explicitly. This is Paper I of the EGESB-G2 Preprint Series. Paper II (G2 compactification): DOI 10.5281/zenodo.19035473. Paper III (SPARC validation): DOI 10.5281/zenodo.18988964. Paper V (predictions): DOI 10.5281/zenodo.18990091.