What question did this study set out to answer?

The research aims to establish a mathematical foundation for the Topological Tension Method (AAM-T) as a tool for structural stability in complex systems.

February 19, 2026Open Access

Topological Tension Method (AAM-T): Dynamic Modulation of Nested Tori and the "Negative Abstract" as a Computable Basis for Structural Stability

Key Points

The research aims to establish a mathematical foundation for the Topological Tension Method (AAM-T) as a tool for structural stability in complex systems.
Developed algorithmic framework for Topological Tension Method (AAM-T)
Modeled complex systems using a multi-level phase geometry of nested tori
Analyzed metric distortions and their effects on phase rigidity
Identified the 'Negative Abstract' as a useful topological defect
Converted high-dimensional projections into a chaos tensor
Maintained system self-regulation within a cognitive attractor zone, optimizing stability

Abstract

Abstract: This paper presents the formal mathematical and algorithmic foundation for the Topological Tension Method (AAM-T) within the framework of Dual-Input Architecture. The model describes complex systems (Artificial Intelligence, Financial Liquidity, Bioinformatics) through a multi-level phase geometry of nested tori. We introduce the concept of the "Negative Abstract" not as a system error, but as a topological defect—a controlled form of uncertainty that prevents phase rigidity (CRYSTAL state). It is demonstrated that metric distortions arising from the projection of high-dimensional topology onto a discrete base are converted into a chaos tensor M-. This process ensures autonomous self-regulation of the system, maintaining it within the cognitive attractor zone of 1/e ≈ 0. 3678. Methodology Identifier: AAM-V1ARTSYBASHEVUAKHARKIVAIANALYSIS

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