The Geometry of Selection and the Measurement of K: A Geometric Theory of Survival in Open Systems

The Universal Selection Operator K encodes irreversible loss in open systems. While introduced abstractly as a non-unitary generator, its physical significance lies in the geometric structure it induces on state space. In this paper I show that K defines a survival geometry: a metric, curvature, and foliation over probability manifolds. Selection is not a force, but a geometric constraint on trajectories. I then demonstrate how K can be operationally measured from time-series data via event statistics, tail exponents, and time–frequency invariants, enabling empirical access to selection landscapes across physical scales.