That means that if you’re connected to the internet through Sprint, you can’t access sites and services hosted by Cogent, and vice versa. It’s Cogent’s fault, as usual, for leeching off of Sprint for too long with a lopsided deal. It will probably be resolved in a few hours or days.
This has happened before: Cogent’s disconnection from Level3 in 2005 was much more severe.
Cogent is terrible, cheap bandwidth, and you should never host anything meaningful on it. It’s so bad that reputable hosts often advertise that they don’t use Cogent bandwidth.
Why Twitter would host their search via Cogent is a mystery to me. I’ll give them the benefit of the doubt and assume they just haven’t gotten to moving it yet since the Summize acquisition, but I’m sure they intended to. Right?