Mathematical Ontology of Causal-Information Reality: The Arhiseme Method and the Fundamental Equation of the Unified World

From the moment of birth we are in intimate contact with the World. We are part of it, and the World speaks to us in Everything. Yet the language with which science describes reality is fractured: the same word — "energy," "information," "subject" — means fundamentally different things in physics, psychology, and philosophy. This crisis of language is the chief obstacle on the path to a unified science of reality. In this work we present the arhiseme method — a systematic procedure for extracting the deepest common semantic kernel (arhiseme) of key interdisciplinary terms and constructing mathematically precise definitions that work equally well in objective and subjective reality. Using this method we build a new unified language, redefining the concepts of information, energy, subject, and object. Drawing on neurophysiological analysis of subjectivity and the subject as a causal-information phenomenon, we formalize Titov's subject-centered model, Tononi's Integrated Information Theory, and a gauge-theoretic approach to neural networks, deriving the fundamental equation of self-organization for causal-information reality. We show that the principle of extremal action, the second law of thermodynamics, the principle of relativity, and Kant's epistemological limit all emerge as special cases. We demonstrate that classical philosophical ontologies (Parmenides, Spinoza, Hegel, Kant) are projections of the unified model and formulate falsifiable predictions, including an experiment on the migration of subjectivity. The Absolute is treated as the ultimate philosophical justification for subject-object dualism. The legitimacy of our approach is reinforced by a direct historical analogy with the creation of infinitesimal calculus: just as Newton's and Leibniz's "infinitesimals" became the language of physics, the arhiseme method aspires to become the language of a unified science of reality.