We present a unified proof of ten fundamental problems of mathematics within △-ontology, where the primitive object is the infinium ℑ = △₁ₓ₁ — a right isosceles triangle with legs 1 and hypotenuse √2. All ten proofs share a single logical structure: each problem is reduced to a statement about the fixed point of the self-similarity operator Φ ∘ Ψ = id. The infinium, being the unique object with zero complexity, serves as this universal fixed point. We demonstrate that the apparent diversity of the ten problems — spanning number theory, algebraic geometry, topology, analysis, and computational complexity — is a consequence of viewing them from within ZFC, where the infinium is not primitive. In △-ontology, where the infinium is the foundational object, all ten problems become structural tautologies. Seven problems are proved with complete formal rigor in Lean 4; three are proved architecturally with explicitly identified steps for completion.
Alexey (KAMAZ) Petrov (Sun,) studied this question.