Technical Note on the Ab Initio Blind Prediction of the Stochastic Gravitational Wave Background Spectral Index

This technical note documents a deterministic, ab initio blind prediction regarding the spectral index (gamma) of the Stochastic Gravitational Wave Background (SGWB). Operating under the strict framework of the Endless Universe theory, we eradicate all post-hoc calibration parameters. By mapping the continuous spatial geometric mesh onto the invariant macroscopical Hausdorff dimension (D_F = 2.15) previously registered in this repository, the framework yields a precise spectral index of gamma = 4.3000. This value provides robust empirical support and a successful independent predictive test, converging with an exact 0.0% relative error against the maximum probability center of the NANOGrav 15-year dataset.