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February 13, 20260 citationsOpen Access

The Ibaguner Fractal Operator (IFO): Hyperbolic Truncuoid Generalization of Conic Pythagorean Structure

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SİSİNAN İBAGÜNER

Key Points

  • The aim is to develop the Ibaguner Fractal Operator (IFO) as a generalization of the conic Pythagorean structure for advanced geometrical analysis.
  • Developed the Ibaguner Fractal Operator using hyperbolic and exponential concepts.
  • Replaced trigonometric generators with hyperbolic generators and exponential lifting.
  • Constructed a mixed curvature decomposition with axial growth and a rotational phase channel.
  • Introduced a hyperbolic truncuoid envelope geometry as opposed to classical conic surfaces.
  • Established a hyperbolic logarithmic operator norm form.
  • Demonstrated fractal scaling behavior within the mixed curvature structure.

Abstract

I introduce the Ibaguner Fractal Operator (IFO)as a hyperbolic–exponential operator generalization of a modified conic Pythagorean–Fermat structure (MPFF). The construction replaces bounded trigonometric generators with hyperbolic generators and exponential lifting, producing a mixed curvature decomposition consisting of an unbounded axial growth channel and a bounded rotational phase channel. The associated geometry is a hyperbolic truncuoid envelope rather than a classical conic surface. A hyperbolic logarithmic operator norm form and fractal scaling behavior are established.  

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SİNAN İBAGÜNER (2026) studied this question.

synapsesocial.com/papers/698ebeb185a1ff6a93016145https://doi.org/10.13140/rg.2.2.15081.35689
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  3. 3The Ibaguner Fractal Operator (IFO): From Basic Analytic Structure to Master Unification2026
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