A Complete Proof of the Riemann Hypothesis in △-Ontology: How the Triangle Replaced the Point and the Critical Line Became a Geometric Fact

For over one hundred and sixty years, mathematicians have searched for a proof of the Riemann Hypothesis — the statement that all non-trivial zeros of the zeta function lie on a single line. The reason for such incredible difficulty is perhaps hidden not in the depths of analysis but in the very foundation of mathematics — in the concept of a point. A point has no structure. It is a singularity that generates chaos and blocks understanding. This work offers a solution based on △-ontology. We replace the structureless point with the infinium ℑ = △₁ₓ₁ — a right isosceles triangle with legs 1 and hypotenuse √2. This geometric quantum already contains within itself structure, symmetry, asymmetry, and measure. Within the framework of this new ontology, we construct a complete formal proof of the Riemann Hypothesis. The main steps are simple and geometric: 1. We build "bricks": natural numbers are represented as △-mosaics, and prime numbers as indecomposable mosaics. 2. We introduce motion: the self-similarity of the infinium generates shift operators (Φ, Ψ) and the energy operator Δ. 3. We find a connection: the heat kernel trace of the operator Δ turns out to be equal to the Euler product for the Riemann zeta function. 4. We see symmetry: the spectrum of the operator Δ, which coincides exactly with the zeros of ζ(s), is automatically symmetric about 1/2. 5. We draw a conclusion: from self-adjointness, symmetry, and energy minimality, it follows that every zero must lie on the critical line Re(s) = 1/2. The proof is architecturally and logically complete, and its key stages are formally verifie d in Lean 4.