The Geometric Form of the Observer Tensor Field: Observation as a Generator of Resonant Geometry

This paper introduces a geometrical formalization of the Observer Tensor Field, extending the foundational Tenson Equation to include the observer as an active geometric agent. Observation, within this framework, is not a passive process but a dynamic act that modulates the curvature of the informational field. We construct the observer-coupled tensor form, define its associated curvature RO, derive the Ricci-contracted form (the Observer Energy–Curvature Equation), and interpret the observation strength parameter λ as a quantifiable measure of informational modulation. Finally, we derive the phase stability condition ℜ(RO) = ℑ(RO) as the equilibrium of energy and information resonance.