This work presents a unified architectural proof of ten fundamental problems of mathematics within the framework of △-ontology, where the foundation is the infinium ℑ = △₁ₓ₁ (a right isosceles triangle with legs 1 and hypotenuse √2). The central statement of the system: ∀ Math ≅ Topos(△₁ₓ₁). All mathematics is isomorphic to a category generated by a single triangle. A detailed RPT-ontology of numbers is introduced for the first time: a natural number is a mosaic of triangles, where primality/compositeness is determined by the presence/absence of a cut along hypotenuse connections. The ten problems include: six unsolved Millennium Problems (P vs NP, Hodge conjecture, Riemann hypothesis, Yang–Mills conjecture, Navier–Stokes equations, BSD conjecture), one solved (Poincaré conjecture), Fermat’s Last Theorem, as well as the Goldbach and Collatz conjectures. All proofs are unified through the use of a single master operator ℋ and the energy principle. The Collatz conjecture receives an intuitive interpretation as an origami process of folding and unfolding △-mosaics. The logical status of the results is fixed through forcing: ℑ ⊩ (all ten problems are true in △-ontology).
Alexey (KAMAZ) Petrov (Tue,) studied this question.