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A measurement being 7 sigma out would still be Chebyshev bounded by 1/7^2 ≈ 0.02 I.e. the probability of it being ≥7 sigma out is interestingly at most 0.02.

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Neat i didn't think about that. But that is less improbable then 1 in 12450197393 which is what you might get with normal distribution.

That's just because Chevyshev bounds is a very weak general statement about all distributions.

High Energy Physics sigma is calibrated to match normal distribution quantiles.

That is not so interesting because it could be far less.

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