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

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-V1_ARTSYBASHEV_UA_KHARKIV_AIANALYSIS