THEORY: OPERATOROLOGY

OPERATOROLOGY: A GENERAL OPERATOR-THEORETIC FRAMEWORK FOR FORMALIZING AND ALGEBRAIZING LOGICAL STRUCTURES, STATE TRANSITIONS, AND SOLUTION SYSTEMS Author: Phan Thành Trung Discipline: Operatorology / Operator Intelligence Keywords: operator theory, dynamical systems, metastability, artificial intelligence, cognitive systems, operator algebra, computational identity. Abstract Classical mathematics represents problems primarily through equations whose solutions correspond to fixed values satisfying functional constraints. While this representation is sufficient for static systems, it is insufficient for modeling complex dynamical systems, cognitive architectures, and artificial intelligence, where stability is defined not by static equality but by persistent invariance under transformation. This paper introduces Operatorology as a general operator-theoretic framework that formalizes and al