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ZENODO
Preprint . 2025
License: CC BY NC ND
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY NC ND
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY NC ND
Data sources: Datacite
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Chaos-Key Simulation Reveals Converging Topological Structure in Nonlinear Chaos

Toward a New Mathematical Framework for Predictable Dynamics in Chaotic Systems
Authors: Moon, Kyung Up;

Chaos-Key Simulation Reveals Converging Topological Structure in Nonlinear Chaos

Abstract

This work introduces the preliminary simulation results of the Chaos‑Key framework—a revolutionary transformation that reveals a deterministic and smooth structure hidden within chaotic systems. The findings challenge long-standing assumptions in mathematics, physics, and nonlinear dynamics, suggesting that chaos may no longer be beyond the reach of closed-form or convergent formulations. The implications are profound: through recursive topological stabilization, the Chaos‑Key function transforms chaotic inputs into predictable, infinitely differentiable outputs. This opens new frontiers in climate modeling, neural system prediction, quantum control, and the foundations of dynamical systems theory. The complete mathematical formulation and algorithmic core—capable of deterministic convergence from chaos—is intentionally withheld to protect intellectual property. Patent applications and international IP procedures are currently underway to prevent unauthorized commercial use, and future publications will disclose the full structure after protection is secured. This release serves as an official public record of academic priority and a signal to the global scientific community. Researchers and institutions interested in collaboration, theoretical expansion, or interdisciplinary application are welcome to make contact.

Keywords

Deterministic Convergence, Chaos Theory, MKU-RDSE, Mathematical Innovation, Predictive Modeling, AI Integration, Topological Stabilization, High-Dimensional Systems, Dynamical Systems, Nonlinear Dynamics, Recursive Systems, FOS: Mathematics, Intellectual Property Protection, Mathematical Physics, Smooth Function Approximation

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green