The Transcendent Periodicity Principle (TTPP), an extension of BSD periodicity, predicts entropy-induced deviations in gravitational wave events. These deviations arise from hidden periodic structures within mass-energy-time harmonics and should be detectable in upcoming LIGO-Virgo-KAGRA (LVK) O4 observations. In this paper, we present testable predictions regarding spectral entropy oscillations and quasi-normal mode (QNM) frequency shifts for different types of mergers: ✔ High-Mass Black Hole Mergers BSD-TTPP predicts entropy-driven deviations in QNM frequencies and a non-monotonic spectral entropy drop post-merger. ✔ Neutron Star Mergers Late-time spectral oscillations should emerge, deviating from current equation-of-state models. ✔ Intermediate-Mass Black Hole Mergers – BSD-TTPP predicts non-linear decay rates for post-merger entropy evolution. These predictions are falsifiable and can be tested against LIGO ongoing O4 observing run (2023-2025).