Vector Field Invariance and Unitary Boundary Transformations in Spacetime Horizons: Resolving the Hawking-Einstein Information Preservation Debate

This paper introduces a vector-field and unitary transformation framework to evaluate space-time horizon transitions at gravitational singularity boundaries. Moving away from stochastic approximations, we project horizon states onto a metric architecture evaluated via the continuous representation of the MH-Shoron Searching Formula (F_MHS). To observe the systemic resilience of this boundary, the empirical coordinate mass vectors calibrated via the Digital Road Method (DRM) are subjected to non-parametric statistical hypothesis testing. The baseline Null Hypothesis (H0), which assumes a chaotic, uniformly distributed dissipation probability (P = 1/9) within the modular boundary, is evaluated against the Alternative Hypothesis (H1). Empirical cross-validation yields a localized Chi-Square Goodness-of-Fit statistic (X^2) of 12.0000 and a Likelihood Ratio Test value (G-Statistic) of 14.9094 across 8 degrees of freedom (df = 8). Python-driven invariant simulations verify that the structural entropy drift registers an Error Coefficient of 0.0, indicating a Hit Ratio of 100% within the tested model parameters. These mathematical outcomes evaluate the chaotic dissipation model against unitary transformation models at the event horizon.