Intrinsic Geometry of Operational Contexts: A Riemannian-Style Framework for Quantum Channels

Abstract

We propose an intrinsic geometric framework on the space of operational contexts, specified by channels, stationary states, and self-preservation functionals. Each context C carries a pointer algebra, internal charges, and a self-consistent configuration minimizing a self-preservation functional. The Hessian of this functional yields an intrinsic metric on charge space, while non-commutative questioning loops dN -> dPhi -> d rho^circ define a notion of curvature. In suitable regimes, this N-Q-S geometry reduces to familiar Fisher-type information metrics and admits charts that resemble Riemannian or Lorentzian space-times. We outline how gauge symmetries and gravitational dynamics can be interpreted as holonomies and consistency conditions in this context geometry.