What question did this study set out to answer?

The aim is to derive the fine-structure constant using a structural expression within the PDL framework.

February 13, 2026Open Access

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

Key Points

The aim is to derive the fine-structure constant using a structural expression within the PDL framework.
Constructed a structural expression for the fine-structure constant using PDL architecture.
Defined relational parameters like valence content and active surface to connect proton and electron properties.
Refined geometrical relations involving the golden ratio to express the fine-structure constant mathematically.
Derived the expression b1^{-1} b5 = bc / (R_{b9} surf^{2}) with bc as the mass ratio of proton to electron.
Achieved a calculated fine-structure constant of approximately 137.02, closely matching the experimental value of 137.036.
Examined the compatibility of the derived expression with the standard Schr46dinger model of hydrogen.

Abstract

We construct a structural expression for the fine-structure constant \ (\) within the Projective Dynamic Logo (PDL) framework. Using the PDL combinatorial architecture of the proton (valence content \ (rₕ₀₋ = 930\), relational sea \ (Rₒ₄₀ = 10\, 087\) ) and a notion of active surface \ (Rₒₔₑ₅\) coupling the proton to the elementary \ ( (4, 6) \) electron block, we postulate \ (^-1 = / Rₒₔₑ₅²\) with \ (= mₚ/mₑ\). A simple geometrical refinement \ (Rₒₔₑ₅ = rₕ₀₋/3\), where \ (\) is the golden ratio, then yields \ (₏₃₋^-1 = \, 9 / (² rₕ₀₋²) \), giving \ (₏₃₋^-1 137. 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.

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