Empirical Detection of the Shadow Corridor (Supporting Analysis)

This paper presents an empirical investigation into a previously unexplained numerical relationship linking prime numbers and fundamental constants. Through large-scale computational analysis, it identifies a narrow structural interval—termed the Shadow Corridor—within which exceptionally precise relationships emerge, while such precision is absent outside it. The study analyzes tens of thousands of prime pairs and shows that high-accuracy relationships are not randomly distributed, but are strongly selected by a common geometric constraint. One particular prime pair is shown to be uniquely distinguished by multiple independent criteria, making it an extreme outlier in precision relative to all others examined. Rather than proposing a new physical theory, the paper documents a discovery process: how a hidden organizing structure was detected empirically before its geometric origin was understood. Subsequent work derives this structure from first principles, and this paper should be read as supporting analysis that records the observational and computational evidence leading to that derivation. To ensure transparency and reproducibility, the complete validation scripts are included. These scripts independently verify all statistical claims, reproduce every figure, and confirm that the reported results are deterministic and repeatable across platforms. This work contributes to ongoing efforts to understand how deep mathematical structure can constrain and organize relationships between number theory, geometry, and fundamental physics. For further information about the ENSO Framework - please contact Eric Needham: ensotheory1@gmail.com Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 International