A Parameter-Free Structural Bridge between the Fine-Structure Constant and Newton's Gravitational Constant in the PDL Framework

Within the Projective Dynamic Logo (PDL) framework, physical reality is reconstructed from relational axioms on finite signed graphs without presupposing space, time, or particles. The proton is represented as a hierarchical composite characterized by the unique integer quintuplet (nᵤ, nd, rₕ₀₋, Rₒ₄₀, Rₓ₎ₓ) = (24, 28, 930, 10, 087, 11, 017) together with a golden-ratio active surface Rₒₔₑ₅ = rₕ₀₋ / 3. From this architecture alone, we derive a structural expression for the fine-structure constant, ₏₃₋, yielding a value that matches experimental data with a relative precision of 1. 0 10^-4 without any continuous fitting parameters. We then demonstrate a structural "bridge formula" connecting the electromagnetic valence surplus rₕ₀₋ to Newton's gravitational constant G. This link is mediated by the primary coherence-leakage parameter G and the 18-fold hierarchical amplification process, recently established as a topological necessity (K₄ S²). These results suggest that fundamental constants are not independent free parameters, but emergent signatures of relational optimization and discrete topological constraints within the PDL substrate.