Unlike previous works, where the reason for the unsolvability of the Hodge Conjecture (as well as the Riemann Hypothesis, P vs NP, Fermat’s Last Theorem, and others) was reduced to a logical contradiction inherent in the structureless point, this article offers a triple diagnosis: energetic, genetic, and architectural. Drawing on the formalism of Δ‑ontology, whose primitive element is the right isosceles triangle △₁ₓ₁ (the Infinitum), we show that: 1. Energetically, the point is the most expensive primitive: it requires infinite memory and computation to specify even the simplest geometric objects. The Infinitum, on the contrary, implements an optimal compression protocol thanks to orthogonality, self‑similarity, and a spectral gap. 2. Genetically, the Infinitum is not an arbitrary figure but the necessary result of a single act of distinction carried out under the principle of minimal complexity. This proves that mathematics built on the point is a historical accident, whereas mathematics built on the triangle is a cognitive and physical necessity. 3. Architecturally, all ten fundamental problems (including the Hodge Conjecture) turn out not to be scattered puzzles but projections of one and the same structural fact — the balance of symmetry and asymmetry in the Infinitum. Their unsolvability in the classical system was predetermined by the fact that they were formulated in a language lacking an inner mechanism for linking the discrete and the continuous. Thus the Hodge Conjecture remained unsolved for a hundred years not because it is “difficult”, but because it was incorrectly posed: it demanded building a bridge between the discrete and the continuous using a tool that itself created the chasm between them.
Alexey (KAMAZ) Petrov (Sun,) studied this question.