It's a one-page short-story, full text available online: http://www.nature.com/nature/journal/v518/n7540/full/518568a.html (Their pdf link also works).
I like the plucky faithful phone, but what does the ending mean? The numbers are presumably dates in seconds, and the second interval is about 30 times longer than the first. Not nuclear war, because the drawer is opened. Maybe Tim changed his mind, or needed independent thought after all?
EDIT Title hints: first adventure suggests a series. I really hope so! Great character, great universe and the singularity onset is an interesting time, if VV has found a way to write about it (he's said post-singularity can't be written intelligibly, hence bobbles and zones). BFF suggests our hero and Tim will be friends (though it's treated ironically in this beginning installment). Clouded view suggests the cloud plays a key role, perhaps as antagonist.
EDIT did some math. Assuming the "dates" are seconds (Vinge also uses this in other stories, including the unix epoch in aDitS). It's suspiciously almost exactly 3,000,000 seconds difference between first and second dates, which is about 35 days - roughly one month. A month fits with Tim's reaction.
It's again an almost exact figure, this time of 95 million seconds between the second and third dates, or 1100 days - a bit over 3 years.
Even better, using the unix epoch, they are 18 Sept 2019, 23 Oct 2019 and 26 Oct 2022. That last one fits with Vinge's estimates of the singularity.
~$ date --date @1568771947 Wed Sep 18 11:59:07 AEST 2019 ~$ date --date @1571772569 Wed Oct 23 06:29:29 AEDT 2019 ~$ date --date @1666762857 Wed Oct 26 16:40:57 AEDT 2022