Trans-Planckian Test of the Effectiveness Principle

This work provides an explicit application and structural consistency test of the Effectiveness Principle introduced in the companion article “The Effectiveness Principle, A Structural Ordering Principle for Physical Counting Under Extreme Conditions”, demonstrating that the trans-Planckian divergence in Hawking radiation arises from structural overcounting rather than from missing high-energy dynamics. The analysis shows that a covariant limitation of physical effectiveness continuously suppresses ultraviolet contributions while leaving the infrared thermal spectrum unchanged. No modification of field equations, dispersion relations, or microscopic degrees of freedom is required. The results indicate that Hawking radiation remains a robust low-energy phenomenon, while trans-Planckian contributions become physically ineffective under extreme near-horizon conditions.