A Structural Derivation of the Fine-Structure Constant from the Projective Dynamic Logo (PDL)

We construct a structural expression for the fine-structure constant \(\alpha\) within the Projective Dynamic Logo (PDL) framework. Using the PDL combinatorial architecture of the proton (valence content \(r_{\mathrm{val}} = 930\), relational sea \(R_{\mathrm{sea}} = 10\,087\)) and a notion of active surface \(R_{\mathrm{surf}}\) coupling the proton to the elementary \((4,6)\) electron block, we postulate \(\alpha^{-1} = \mu / R_{\mathrm{surf}}^2\) with \(\mu = m_p/m_e\). A simple geometrical refinement \(R_{\mathrm{surf}} = \varphi r_{\mathrm{val}}/3\), where \(\varphi\) is the golden ratio, then yields \(\alpha_{\mathrm{PDL}}^{-1} = \mu\,9 / (\varphi^2 r_{\mathrm{val}}^2)\), giving \(\alpha_{\mathrm{PDL}}^{-1} \simeq 137.02\) in close agreement with the experimental value \(137.036\) without any continuous fit parameter. We analyse the assumptions, local robustness, and compatibility of this expression with the standard Schrödinger description of the hydrogen atom.