Unifying General Relativity and Quantum Mechanics in Δ‑Ontology: From the Structureless Point to the Structural Quantum △₁ₓ₁

Abstract

This paper examines one of the central problems of modern physics—the absence of a unified theory combining general relativity (GR) and quantum mechanics (QM). It is shown that the reason for this unresolved problem lies not in physics as such but in the mathematical foundation: both theories are built on the structureless point, which does not contain a connection between the discrete and the continuous. Within Δ‑ontology, where the first principle is the right isosceles triangle △₁ₓ₁ with legs 1 and hypotenuse √2, this connection is already embedded geometrically. GR turns out to be a projection of the infinium onto the continuous component (the hypotenuse), and QM a projection onto the discrete component (the legs). Their unification is achieved not through artificial quantization of gravity but through a return to the common geometric root—the Pythagorean theorem. The paper explains step by step how space‑time, quanta, and gravity arise from the infinium and how Einstein’s two theories become two limiting cases of a single △‑mosaic.