Published September 1, 2025 | Version v3
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Alpha

Description

In this paper, I derive the fine-structure constant $\alpha$ as an emergent and parameter-free invariant of Relator theory. The construction uses the Schrödinger equation, classical electrodynamics and mechanics, and Relator geometry with luminal evolution on the   $\mathbb{C}$-space and the orthogonal spatial sector $\mathbb{R}^3$, which fixes a minimal phase cavity and the Coulombic baseline. A transverse traceless inductive channel is incorporated through a UV, IR, and OUT decomposition, and a logarithmic closure uniquely determines $\alpha$ with no fitted numbers and with no use of measured constants $e$, $c$, and $\hbar$. No quantum electrodynamics is invoked at any stage. The prediction matches the most precise independent measurements at sub-ppt accuracy and remains stable under regulator choices and multipole cutoffs.

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Subtitle
The Fine-Structure Constant Emergent