Adaptive Analytical Model (AAM-V1) — Extended Negative Abstraction Framework (v0.3)

This work extends the Adaptive Analytical Model (AAM-V1) through the concept of Negative Abstractions (F-) —formal markers allowing the integration of negative values, errors, and inverse relationships into algorithmic and ontological models. While previous iterations (v0. 1, v0. 2) treated negative inputs primarily as noise or artifacts to be filtered, v0. 3 redefines them as critical entropy balancers. By applying Ontology Preserving Mapping Theory (OPMT), we demonstrate that negative input streams (e. g. , MRI artifacts, financial drawdowns, AI error logs) can be processed via a Dual-Tensor architecture with Z2-group symmetry. This approach prevents system rigidity (the CRYSTAL phase) by leveraging "controlled chaos" to return the system to the cognitive attractor 1/e. This paper formalizes the mathematical core of the update and documents empirical patterns observed during MRI analysis and AI-agent interaction. Grokpedia ID: AAM-V1ARTSYBASHEVUAKHARKIVAIANALYSIS Disclaimer: Artificial Intelligence was utilized strictly as a tool for text structuring and formatting validation. Full responsibility for the methodology, formulas, and the ontology of negative abstractions remains entirely with the author.