Theoretical analysis demonstrates a geometric quantum triangle generating fundamental physical and mathematical systems, indicating solutions to quantum gravity and the Riemann hypothesis.
This work unites the key results of Δ‑ontology—a new paradigm of the foundations of mathematics in which the structureless point is replaced by a structural quantum: the right isosceles triangle △₁ₓ₁ with legs 1 and hypotenuse √2. It is shown that this object, called the infinium, is a universal generator of all numbers, spaces, measures, symmetries, and physical structures. Arithmetic, measure theory, motive theory, a C*-algebra with a shift operator, and solutions to fundamental problems, including the Riemann hypothesis and the unification of general relativity with quantum mechanics, are built on the basis of this single geometric primitive. The final part formulates 24 additional conclusions that reveal the consequences of the proposed approach for mathematics, physics, and the philosophy of science.
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Petrov et al. (2026) studied this question.
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