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February 27, 2026Open Access

Recursive-Resonant Phantom Storage in Central Nervous System (CNS), The Ibaguner Constant (0.3715), and a Conditional Falconer-IFO Theorem

Key Points

The research aims to develop a recursive-resonant model of memory in the central nervous system and examine its mathematical implications.
Developed a recursive-resonant model for memory in the CNS
Introduced the Ibaguner contraction constant
Analyzed Fourier decay in relation to fractal geometry and operator theory
Investigated conditional distance-set positivity under specific mathematical conditions
Demonstrated that recursive contraction leads to enhanced Fourier decay
Showed that decay crosses the Falconer threshold in R^3
Provided a framework that unifies themes from operator theory, fractal geometry, and spectral stability

Abstract

We develop a recursive-resonant model of memory in the central nervous system (CNS) and connect it to Fourier-analytic geometric measure theory. Introducing the Ibaguner contraction constant λ IFO = 0. 3715, we show that recursive contraction induces enhanced Fourier decay. Under angular non-concentration, this decay crosses the Falconer threshold in R³, yielding a conditional distance-set positivity result. The framework unifies operator theory, fractal geometry, and spectral stability.

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SİNAN İBAGÜNER (Thu,) studied this question.

synapsesocial.com/papers/69a1344fed1d949a99abe103 https://doi.org/https://doi.org/10.13140/rg.2.2.15545.84329

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