Formal Verification in Lean 4.The Ten Bridges Theorem: A Unified Architectural Proof of Ten Fundamental Problems of Mathematics in △-Ontology via the Infinium as the Most Powerful Invariant

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. It is shown that all ten problems – six unsolved Millennium Problems (P vs NP, the Hodge conjecture, the Riemann hypothesis, the Yang–Mills conjecture, the Navier–Stokes equations, the BSD conjecture), one solved (the Poincaré conjecture), Fermat's Last Theorem, as well as the Goldbach and Collatz problems – are not independent hypotheses but projections of a single geometric fact: the balance of symmetry and asymmetry encoded in the infinium. The proofs are unified through the master operator ℋ, the energy principle, and the method of kinematic paths. The infinium serves as the fixed point of the self-similarity operator (Φ ∘ Ψ = id), through which all ten problems are visible. Formal verification is carried out in Lean 4.