What question did this study set out to answer?

The aim is to derive the fine structure constant from first principles using a new geometric framework.

February 16, 2026Open Access

Critical Planckian Spin Dynamics: Geometric Derivation of the Fine Structure Constant.

Key Points

The aim is to derive the fine structure constant from first principles using a new geometric framework.
Developed a framework called Critical Planckian Spin Dynamics (CPSD) based on five irreducible axioms.
Analyzed the unique compatible 4D polytope known as the 600-cell.
Conducted electromagnetic resonance analysis to estimate optimal parameters.
Derived the fine structure constant $ ext{α}^{-1}=137.036$ with high precision.
Achieved an optimal parameter $N_{opt}=137.035999206$, closely matching $ ext{α}^{-1}$ within experimental uncertainty.
The theory has zero free parameters and introduces the golden ratio as a key geometric concept.

Abstract

We present Critical Planckian Spin Dynamics (CPSD), a geometric framework deriving the fine structure constant ^-1=137. 036 from first principles. Starting from five irreducible axioms, we prove the 600-cell is the unique compatible 4D polytope. Electromagnetic resonance analysis yields N₎₏ₓ=137. 035999206, matching ^-1 within experimental uncertainty. The theory contains zero free parameters and incorporates the golden ratio as a geometric consequence.

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