tldr; of the article: clocks were synced using satellites whose velocity led to slight relativistic changes in the times sent out, fully accounting for the 60 nanosecond difference.
Except...
Well, for one thing those sorts of corrections are so basic to the system they are built into it. The idea that it wasn't taken into account in a system designed to give 20cm resolution... yeah, not buying it.
For another, this kinda fails the smell test. The author is a theorist working in AI and the paper reads like an undergraduate attempt to get the rights numbers out of a special relativity problem. The proposed error is incredibly simple, theory wise, and yet was supposedly missed by the 175 physicist co-authors of the original paper during their six months sanity checking the result.
Finally, it looks to me like he is assuming the clock used for timing was the one on the GPS satellite. That is simply wrong. The group used a pair of atomic clocks
synchronised by GPS. GPS satellites themselves have frequency correction so they are keeping earth time, so if you receive a GPS signal the only adjustment from that you need to make is for transmission time.
Most of the experimentalists I follow are very unimpressed. Try
Tom (who works with atomic clocks), his
follow up about time synch or
Chad for the standard responses.
I'm buying the majority view here that this is going to be a hard to find error deep in their code or something interesting in the decay physics rather than the neutrino speed itself. But it's
probably not a weak quantum measurement effect.