The disagreement-detection lower-bound conjecture for multi-value Byzantine agreement

Let $k$ nodes each be assigned an arbitrary initial value of $l$ bits. A node detects disagreement if the initial values are not all identical.

Disagreement-detection lower-bound conjecture. If the $k$ initial values are not identical, at least one node can detect this only after at least

$$(k-1)l$$

bits have been communicated.

This auxiliary conjecture is proposed as the basis for the communication lower bound used to argue optimality of the paper's Byzantine agreement algorithm. The supplied text gives no proof or resolution of it.