Thellim isn't sure why this question is arising in the middle of the question about whether or not dath ilan is going to conquer Earth, but she has obviously taken a prior interest in this question.
There's a mage supposedly training himself now, to settle FTL questions once and for all. But in terms of experiments that could be done with mages and psions that happen to already exist... there's been improvised experiments with remote-viewing clocks on the other side of the planet. There's been improvised experiments with an ancient highly-practiced weather-mage who can stir a wind on the other side of the world. All such experiments have "failed to produce statistically significant evidence" of a 20-millisecond difference depending on whether the target is next door, or on the opposite side of the Earth.
Earth is sufficiently confused about how evidence works that Earth scientists have not dared to try to say to reporters that this looks like magic is FTL. Thellim has gotten ahold of the raw data and treated it with sane numerical procedures, and derived strong-enough likelihood ratios against 20-millisecond delays; real epistemology is quite capable of saying that an effect size has been ruled out, not just that somebody failed to produce statistically significant evidence for any effect size.
[FTL information reception: 0.99y/0.01n
FTL causal manipulation: 0.98y/0.02n
FTL counterfactual information reception: ~1y/~0n, reminder: precognition is a thing]
Thellim doesn't transmit back the reasons. If the Keeper wanted to reconsider her reasons and not just the final summary probabilities, he'd have asked her for her reasons. It feels so nice to talk again with somebody who knows what it even means to trust her sometimes.