Email: infinium.science@mail.ru Saratov

Part II: The Space of Two‑Dimensional △‑Mosaics, the Groupoid, and the C*-Algebra

This work is the second stage of the program begun in Part I. Whereas Part I constructed and fully investigated the linear (one‑dimensional) model of △‑chains, here we lay the foundation for the basic — two‑dimensional — model of Δ‑ontology. This necessity is dictated both by mat...

Part I: An Operator Model Based on Self‑Similar Triangular Mosaics: Arithmetic, Shift Operator, and Spectrum

Within the framework of Δ‑ontology, where the basic primitive instead of the structureless point is the right isosceles triangle △₁ₓ₁ with legs 1 and hypotenuse √2, an operator model is constructed that unifies arithmetic and spectral analysis. Natural numbers are represented by...