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Although the scalar nonlinear Schrodinger equation has provided valuable insights into how quantum mechanics might modify the classical general relativistic description of space-time, a detailed understanding of space-times with matter has remained elusive. In this paper, we propose generalizing the nonlinear Schrodinger equation theory of Einstein spaces to include matter by transplanting the 3 + 1 dimensional theory to the 24-dimensional Leech lattice plus 1 time dimension. The scalar wave function and Chern-Simons gauge potential which encode the classical Kahler potential become 11 × 11 complex matrices belonging to a 195,442 dimensional representation of the Mathieu group M11. This theory describes gravity coupled to internal degrees of freedom which include a supersymmetric E6 × E6 Yang-Mills theory of matter.

Leech Lattice Extension of the Non-Linear Schrodinger Equation Theory of Einstein Spaces