A Closed-Form Identity for the Ratio of Iterated Exponential Integrals

I am pleased to announce the numerical discovery of a non-trivial sequence of complex zeros for the entire function H(u), associated with the mathematical constant x_0 \approx 1.7756. Using high-precision computational methods (precision up to 10^{-50}), I have mapped the first seven pairs of complex zeros in the left-half plane, revealing a highly structured asymptotic trajectory with a characteristic vertical spacing of \Delta Im \approx 2\pi. This finding provides a new numerical foundation for the analytical study of H(u) and its periodic properties. Please note that this is a preliminary announcement of the discovery; a comprehensive research paper containing the full analytical derivation, expanded zero-maps, and the final asymptotic formula will be uploaded in the near future.