What question did this study set out to answer?

The aim is to derive fundamental aspects of emergent spacetime from a weighted entanglement lattice framework.

March 18, 2026Open Access

The Entanglement Lattice Substrate and Emergent Spacetime

Key Points

The aim is to derive fundamental aspects of emergent spacetime from a weighted entanglement lattice framework.
Develop the entanglement lattice with ~10^180 nodes and derive key mathematical structures.
Derive the bulk Lagrangian, Euler-Lagrange equations, and effective cosmological constant.
Utilize max-flow min-cut for the Ryu-Takayanagi formula and graph Laplacian spectral coarse-graining.
Achieved the Einstein equations through a thermodynamic approach.
Identified a modified Friedmann equation with parameters w0=-0.97, wa=-0.14.
Derived emergent time and identified open problems for future research.

Abstract

We present the complete foundational mathematics of EGESB-G2 Level 1. From the weighted entanglement lattice B= (V, E, W) with N~10¹80 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.

The Entanglement Lattice Substrate and Emergent Spacetime

Key Points

Abstract

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