ANSI X9.31: the purpose of the date/time vector in the PRNG? What is the exact purpose of the date/time vector $dt$ in the ANSI X9.31 PRNG?

$$ I := E_K(dt) $$
 $$ R := E_K(I \oplus V_{old}) $$
 $$ V_{new} := E_K(R \oplus I) $$

Specifically, the document seems to imply that the seed $V_*$ and key $K$ must be kept secret, but makes no claims on the secrecy of the $dt$ vector, only that it should be increased on each iteration. Can it be known by an adversary? Are there any implications if it is known to an adversary?
From ANSI X9.31:1988, Appendix A.2.4 (Generating Pseudo Random Numbers Using the DEA):

"Let DT be a date/time vector which is updated on each iteration."

The purpose of $dt$ is to supply a value that is different each time the algorithm is seeded, so as to generates a different sequence, even if $V_*$ (the initial value of $V_{old}$) is a fixed secret.

The algorithm seems to be secure even if $dt$ is known, and predictable, e.g. a 64-bit counter starting from 0; at least, that's the design goal. However it must not be possible to return $dt$ to an earlier value. In other words, $dt$ needs to be a "number used once", sometime called nonce.

Beware that an adversary could set the clock, hence $dt$. In the absence of a specific mechanism, that might allow her to re-generate a previous sequence!

It is probably best if the adversary can not choose $dt$ (and that makes it much easier to insure that $dt$ is unique).