The Allende Conjecture: Structural Selection in the Modular Space

This work presents the Allende Conjecture, a mathematical conjecture concerning structural selection in the modular space of elliptic curves with Complex Multiplication (CM). Restricting the domain to the two primary CM points, j = 0 and j = 1728, we introduce an explicit constraint: the requirement of an orthogonal basis for torsional information processing. Under this constraint, the quadrangular lattice corresponding to j = 1728 is uniquely selected, while the hexagonal lattice is excluded. The result is purely structural and informational, does not imply physical causation, and may be interpreted as a reduction of algorithmic description length under explicit constraints.