Proof of the Hodge Conjecture using different methods and approaches

The Hodge conjecture states in one of its most common forms that all Hodge classes on smooth projective algebraic non-complex geometric figures resp. varieties do possess algebraic cycles and that all Hodge classes on holomorphic projective algebraic complex geometric figures resp. varieties are algebraic and do have algebraic cycles as well. This conjecture was established by the Scottish mathematician William Vallance Douglas Hodge in the 1930s. The Hodge conjecture could not generically be proved to be true up till this day but only for some special cases. In this research paper, we have firstly proved the Hodge conjecture using the infinitesimal lines approach combining the usage of mathematical frameworks like nonstandard analysis and differential geometry. Then we have conducted a more generic proof of the Hodge conjecture without relying on specific mathematical frameworks by showing that all Hodge classes on smooth projective algebraic non-complex geometric figures resp. varieties and all Hodge classes on holomorphic projective algebraic complex geometric figures resp. varieties are just a subset of all existing algebraic varieties which do have algebraic cycles.