This question, about the fairness of a 7-sided die, troubles me.
It is in my opinion well-thought out and well-formulated. It is asking if a particular die has had any sort of rigorous analysis (physics-based or statistics-based) performed to test its fairness. That is simple, direct, and if such analysis had been done would lead to an answer of, "Yes, see this link," and a paraphrase.
It also seems directly on topic: We have tags for dice, for statistics, and for scientific-validation, all of which apply. (Although... why do we have a tag for scientific-validation? That is the only question with that tag. What's up with that, exactly?) Two of those tags, at least, are properly employed, so I will view, "This is off-topic," somewhat skeptically.
On the other hand, to the best of anyone's knowledge, the analysis does not exist. But negatives are hard to prove, so a technically correct answer is wishy-washy and time-limited at best: "So far as we know, as of the date of this answer... no analysis, so we don't know."
Further, the answers generated are really poor. In particular, there is an analysis that is really a series of assertions, with no source or reference, and which is basically wrong. A peer-reviewed article can show that the assertion/analysis is wrong, but can't (and doesn't purport to) provide a real answer to the question other than, "It could be."
I am qualified to summarize that peer reviewed article, but haven't done so because I still can't answer the question, I can only attack an existing answer. Perhaps I am wrong, but this seems out of bounds for an answer.
What to do?
