Universal Coherence Leakage: Bridging Gravitational and Fine-Structure Constants through Discrete Relational Closures

This paper presents a landmark unification within the Projective Dynamic Logo (PDL) framework, demonstrating that the gravitational constant $G$ and the fine-structure constant $\alpha$ emerge from a single combinatorial necessity: the coherence leakage ($\varepsilon$) of the protonic system $(24, 28, 930, 10087, 11017)$. By inverting the 18-stage hierarchical filtering law associated with gravity, we derive a foundational leakage parameter $\varepsilon_G \approx 0.007389$. We show that the experimental deviation of the fine-structure constant from its ideal integer-valence form is numerically "locked" to this gravitational leakage through a geometric bridge involving the golden ratio ($\phi$) and the three-fold valence core. This work suggests that physical constants are not independent empirical inputs but are rigid consequences of the discrete logical architecture of the proton, providing a fully relational and deductive path toward the emergence of physical law.