Observer Geometry G; The Universe as a Self-Observing System: Algebraic Structures of Self-Referential Cosmology

This paper proposes a theoretical framework that models the universe as a selfobserving system. By treating the observer algebra and the observed system algebra as different realizations of the same noncommutative algebra, the mathematicalfoundation of self-referential cosmology is established. Within this framework, thecosmological constant is reinterpreted as the normalized trace of the observationbackreaction operator, and the natural smallness of its value originates from the reciprocal relationship with the total entropy of the universe. We further prove thatdifferent realizations of the multiverse correspond to Morita equivalence classes ofthe observer algebra, while observable cosmological parameters are constrained byself-referential consistency conditions. This theory predicts specific non-Gaussianitypatterns in the cosmic microwave background, characterized by oscillatory structures in the three-point correlation function, which can be tested by next-generationcosmological experiments.