The ABCD hypothesis, formulated by Chan, Jackson and Trang, is the conjunction of $ZF$ and the statement: (*) given four infinite cardinals $A, B, C, D$, then $|A^B| \leq |C^D|$ if and only if $A\leq C$ and $B\leq D$. Recently W. Chan shows that $AD^+$ implies (*) holds below $\Theta$. We sketch a scenario to improve this result and show the full ABCD hypothesis is consistent. This is not a complete proof as it relies on conjectures about the structure theory of Nairian models but presents the most plausible path towards the consistency proof.