W* = e⁻¹ as a Universal Critical Exponent: Geometric Foundation and Multi-Domain Empirical Support

We present a convergent argument that $W^{*}=e^{-1}\approx0.36788$ is a universal critical exponent for a class of coherence-fragility transitions across physically unrelated domains. The argument rests on three independent foundations: (1) an analytical derivation from a first-principles entropic flow equation, where $W^{*}$ is the unique stable fixed point; (2) a geometric derivation from dissipative category theory and Filippov-Ricci curvature flow, where $W^{*}$ emerges as the locus of zero curvature a structural necessity, not a parameter; and (3) empirical consistency across seven independent domains nuclear reactor safety, oncological pathway coherence, plasma disruption detection, electricity grid reliability, Earth system tipping elements, cognitive decision thresholds, and classical orbital mechanics without recalibration between domains. A universality class conjecture is stated precisely. The closed-form structural validity window $\tau_{collapse}=-Ei(1+log W_{0})/(\kappa e),$ where Ei is the exponential integral and $K=3/2$, characterises the time-to-irreversibility for systems below $W^{*}$.