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, rᵥₐₗ, Rₛₑₐ, Rₜₒₜ) = (24, 28, 930, 10,087, 11,017) together with a golden-ratio active surface Rsurf = φ · rᵥₐₗ / 3. From this architecture alone, we derive a structural expression for the fine-structure constant, αPDL, 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 Δ rᵥₐₗ to Newton's gravitational constant G. This link is mediated by the primary coherence-leakage parameter εG 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.