My updated list after some more work yesterday is

96286, 9344, 107278, 68204, 905, 23565, 8415, 62718, 83512, 16423, 42742, 94304

which I see is the same as simon’s list, with very slight differences in the order

More on my process:

I initially modeled location just by a k nearest neighbors calculation, assuming that a site’s location value equals the average residual of its k nearest neighbors (with location transformed to Cartesian coordinates). That, along with linear regression predicting log(Performance), got me my first list of answers. I figured that list was probably good enough to pass the challenge: the sites’ predicted performance had a decent buffer over the required cutoff, the known sites with large predicted values did mostly have negative residuals but they were only about ^{1}⁄_{3} the size of the buffer, there were some sites with large negative residuals but none among the sites with high predicted values and I probably even had a big enough buffer to withstand 1 of them sneaking in, and the nearest neighbors approach was likely to mainly err by giving overly middling values to sites near a sharp border (averaging across neighbors on both sides of the border) which would cause me to miss some good sites but not to include any bad sites. So it seemed fine to stop my work there.

Yesterday I went back and looked at the residuals and added some more handcrafted variables to my model to account for any visible patterns. The biggest was the sharp cutoff at Latitude +-36. I also changed my rescaling of Murphy’s Constant (because my previous attempt had negative residuals for low Murphy values), added a quadratic term to my rescaling of Local Value of Pi (because the dropoff from 3.15 isn’t linear), added a Shortitude cutoff at 45, and added a cos(Longitude-50) variable. Still kept the nearest neighbors calculation to account for any other location relevance (there is a little but much less now). That left me with 4 nines of correlation between predicted & actual performance, residuals near zero for the highest predicted sites in the training set, and this new list of sites. My previous lists of sites still seem good enough, but this one looks better.

On one interpretation of the question: if you’re hallucinating then you aren’t in fact seeing ghosts, you’re just imagining that you’re seeing ghosts. The question isn’t asking about those scenarios, it’s only asking what you should believe in the scenarios where you really do see ghosts.