The Fractal Coupling Flow of the Minimal Discrete Épure

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Authors: Florian Gisbert
Cited by: 22
References: 5

Abstract

We study how the electromagnetic fine-structure constant may arise from the combinatorial structure of the Minimal Discrete Épure G■=(Z²,d■). The framework rests on a single empirical input (spacetime dimension d=4) and an operational definition of the electromagnetic coupling within the épure formalism. The anisotropy parameter ξ₂=37/1296 is shown to be derived from the cost asymmetry (1,2) alone, independently of α, and the two resummation coefficients are given geometric origins. The fractal resummation yields 1/α_EM≈137.036. Epistemic status: the formula is presented as a rigorously supported numerical conjecture. Its theoretical derivation — the form of the Dyson-type resummation — is identified as the central open problem of the programme. All results verified in Python 3.

Fields of Study & Subjects

Advanced Mathematical Theories and Applications Advanced Mathematical Theories Theoretical and Computational Physics

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
21 June 2026
Language
EN
Document type
Preprint