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The Ibaguner–Euler Constant: Variational Recursion Threshold, Spectral Structure, and Thermodynamic Bifurcation in the Ibaguner Fractal Operator

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Authors: SİNAN İBAGÜNER

Year

2026

Paper ID

25455

Status

Preprint

Abstract Read

~2 min

Abstract Words

98

Citations

N/A

Abstract

We present a comprehensive mathematical formulation of the Ibaguner Fractal Operator (IFO) as a nonlinear exponential recursion derived from a variational free-energy principle. We prove that the maximal recursion intensity admitting real equilibria equals αIE = 1/e, termed the Ibaguner–Euler constant. This constant emerges simultaneously as a variational extremum, a saddle–node bifurcation threshold, a spectral degeneracy point, and a thermodynamic balance constant. Discrete and continuous formulations are analyzed, a renormalization structure is outlined, and stability properties are established. The result situates the IFO within nonlinear dynamics while preserving its interpretive role in the Quantum–Mathematical Trinity framework.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • We present a comprehensive mathematical formulation of the Ibaguner Fractal Operator (IFO) as a nonlinear exponential recursion derived from a variational free-energy principle.

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References & Citation Signals

[1] DOI https://doi.org/10.5281/zenodo.18843177 [2] Publisher https://doi.org/10.5281/zenodo.18843177

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