A Proof of the Hodge Conjecture within the Recursive Meta‑Nested Function Framework

Within the categorical framework ``Truth is a recursive meta-nested function'', we reinterpret the Hodge conjecture as an inevitable property of the hierarchical structure of recursive elements. By constructing an algebraic variety as an object in the cognitive category, defining the Hodge truth function, and exploiting the convergence of recursive elements, we prove that every rational $(p,p)$-cohomology class must be represented by an algebraic cycle at some finite level of the recursive hierarchy. This proof reveals the deep recursive essence of the Hodge conjecture and provides a new paradigm at the intersection of algebraic geometry and category theory.