Consciousness-Extended Einstein Equations: A Minimal Geometric Framework for Mind-Matter Coupling (Part I) - Revised and Expanded

Abstract: We advance the hypothesis that information integration—a measurable feature of awareness—can weakly source spacetime curvature. Within an effective field theory (EFT) framework, we construct a covariant, minimal extension of Einstein's equations in which an information-source field Phi(x^mu), a relational awareness matrix R, and quantum matter are geometrically coupled through a five-sector action. The multipartite total correlation (MTC) serves as an operational proxy for integrated information: Phi[S] = Sum( S(rho_i) ) - S(rho_S) (Where S(rho) = -Tr[rho log rho] is the von Neumann entropy ). Five independent coupling channels (alpha, beta, gamma, zeta, lambda) connect to curvature, awareness coherence, matter density, axial spin current, and vorticity respectively. The framework is consistent with all present empirical bounds for small couplings. Every coupling channel admits null-result tests, providing clear falsifiability at precision-metrology sensitivities of order 10^-18. We discuss the relationship to Part II (topological neurodynamics) and Part III (unified predictions and experimental roadmap). Keywords: general relativity; consciousness; information field; effective field theory; Einstein equations; integrated information; multipartite total correlation; spacetime curvature; mind-matter coupling. Mathematical Subject Classification (2020): 83C05, 81T13, 94A17, 92C20, 83C45.