From the Infinitum (Right Isosceles Triangle, RIT) △₁ₓ₁ to the Hodge Conjecture, Part 2: Formal Proof, Explicit Examples, and Computational Algorithms

This paper is a direct continuation of "From the Infinitum (Right Isosceles Triangle, RIT) △₁ₓ₁ to the Hodge Conjecture: 𝔹‑Structures, Motives, and an Explicit Formula for Algebraic Cycles" (Part 1). Part 1 introduced the general formalism of 𝔹‑structures and 𝔹‑motives; the present Part 2 provides the complete formal proof of the Hodge conjecture within that framework, analyses the algorithmic complexity of the construction, illustrates the theory with fully worked‑out examples (projective spaces, elliptic curves), develops the harmonic theory of 𝔹‑cohomology, and shows how to construct universal 𝔹‑manifolds whose cohomology realises any prescribed simple 𝔹‑module. Together, the two parts turn the Hodge conjecture from an existence problem into an explicit, computable procedure.