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

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 in objective and subjective reality. Using this method, we redefine the concepts of information, energy, subject, and object. Drawing on Titov's subject-centred model, Tononi's Integrated Information Theory, and gauge-theoretic approaches to neural networks, we derive the fundamental equation of self-organisation 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. Classical philosophical ontologies (Parmenides, Spinoza, Hegel, Kant) are demonstrated to be projections of the unified model. Falsifiable predictions are formulated, including an experiment on the migration of subjectivity via a shared interface. The Absolute is treated as the ultimate philosophical justification for subject–object dualism. A machine-verified Lean 4 proof is provided.