Publishing the number would not in any way, alleviate the concern that the system was not fair. You are thinking about this problem from a mathematics stand point when the issue is a social one.

I plead guilty to approaching from a mathematics PoV. My sole intent is to overcome the tyranny of distance and exploitation of the time difference. The only people I hope to convince are other, mathematically sophisticated traders. By social do you mean the public-at-large's suspicion?

1, 1, 1, 1, 1... Can you verify if this sequence is random or not?

OK, I'm lets stipulate that I am not particularly mathematically sophisticated.

However, I thought that you had a list of numbers at least as large as the number of trades expected in the 5 minute period, then you could order the trades by shuffling the numbers. I think it would not be too taxing to determine whether the sequence over time is random enough.

That said, I'm starting to see whether that it would impossible to know whether any particular 5 minute (or maybe day's worth) of trading is random enough. Perhaps crypto can come to the rescue here. Publish lists of random numbers in advance pgp signed.

Anyway, enough of my ramblings :-)