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.