On the Tendency of Physical Systems to Form Varieties; and on the Perpetuation of Structure by Universal Natural Selection

Selection under irreversible loss is identified as a primitive mathematical structure underlying measurement, persistence, and correlation constraints across physical domains. A log-moment selection load is introduced as the fundamental object governing survival-conditioned statistics, with mean hazard recovered as a first-cumulant approximation. It is proven that nontrivial locally factorizable selection kernels are incompatible with exact no-signaling, yielding an emptiness theorem for local selection under causal consistency. By contrast, globally coordinated selection kernels admit no-signaling distributions exceeding the Tsirelson bound. These results establish quantum correlations as the extremal admissible regime of selection subject to local implementability and global normalization, without invoking Hilbert-space axioms.