Formal uncertainty principle implies duality

Let $A$ and $B$ be theories, and let $\Delta A$ and $\Delta B$ denote their formal uncertainties. Suppose that $l>0$.

Formal uncertainty–duality conjecture. If $A$ and $B$ satisfy

$$\Delta A\,\Delta B\geq l>0,$$

then they correspond to dual theories.

This conjecture proposes that a formal uncertainty principle is sufficient for duality. The surrounding discussion emphasizes that the converse need not hold: dual theories can exhibit a formal uncertainty principle through deconstruction and reconstruction without necessarily satisfying a traditional uncertainty principle. The status of the proposed implication is not resolved in the supplied text.