The Blind Spot of a Century: Why the Point Itself Made the Hodge Conjecture Unsolvable, and How the Infinitum Dissolves the Deadlock

This paper does not offer yet another proof of the Hodge Conjecture within the standard axiomatic framework. Instead, it identifies a deeper obstruction that has kept this and other fundamental problems (the Riemann Hypothesis, P vs NP, Fermat's Last Theorem before Wiles) unresolved for decades despite enormous intellectual and financial investment. We argue that the root cause is not the intrinsic complexity of these problems but a logical flaw embedded in the very foundation of mathematics: the use of a dimensionless, structureless point as the primitive element. As an alternative, we present Δ‑ontology, where the foundational object is the structural quantum known as the Infinitum — the right isosceles triangle (RIT). We demonstrate how this shift naturally dissolves the contradictions that made the classical problems intractable, and why, from the Δ‑ontological standpoint, the Hodge Conjecture becomes a tautological consequence of defining number through geometric mosaics.