The Gemara is discussing the problem if contradictory witnesses being suspect for future testimony, particularly under Rav Chisda's opinion.

The Gemara tells us on the top of 48a, likely restating a case from Rosh Hashana ch 2, about the situation where one witness claiming the height of the moon at 2 units and another witness claiming the height of 3 units. We can join these two witnesses into one group of witnesses, and they remain trustworthy.

As I will continue to ask below, is the reason that they are allowed to join despite saying different testimony because there is a rounding error, or they are within the same "tolerance" of error of measurement?

If the most precise measurement device would say 2.5 units, and one had rounded up, and the other had rounded down, each could be reporting accurately, and thus it is possible that they are both truthful and sufficiently accurate?

Or perhaps just like time measurements in halacha (per Rabbi Chaim Goldberger - context was date of time of death with chezkas chaim) are always seen with an error tolerance of 2 minutes, perhaps height measurements also have a tolerance?

Regardless of why they join, we know they do.

Then comes the Gemara's next case that one says 3 units, and the other says 5 units. They are contradictory and cannot be joined. Presumably being off by 2 units is too far off to reconcile by either a rounding error or required precision. We cannot see them as reconcilable.

After this I think the Gemara tells us that if a third person comes along and concurs with one of the first two, that they then form a group, but the other one is now suspect for future testimony.

With that, here comes my question:

The Gemara does not specifically address this, I am asking how we would deal with a hypothetical situation, and seeing if it helps us to better understand what the Gemara did tell us.

What if the third person who came along claimed the moon was at height 4 units?

It would seem that we could join this third person with either of the first two, since by either reason that 2 and 3 could join in the first case, 3 and 4 can join, or 4 and 5 can join.

In mathematics we have the transitive property. If we apply it here we get a contradiction.

We know that 3 and 5 cannot be on the same team, but 3 is close enough to 4, and 4 is close enough to 5, that perhaps by the transitive property, 3 and 5 are close enough if there is also a 4 on the team? But that would conflict with the principle of seeing 3 and 5 as irreconcilable.

If the purpose of allowing a third witness to join with one of the first two is because the Gemara wants to keep at least one of the two witnesses trustworthy, how would Beis Din decide which one to keep, and which one to make untrustworthy, if the only information we have is 3, 5, and 4 -- 4 is no closer to 3 or 5, so on what basis could they make this choice?

Or, could Beis Din use the transitive property and in this case accept 2 outliers?

If the reason we allow 2 and 3 to join is because we allow a rounding error, that we see it as the truth being 2.5, the average of the 2 claims, and both 2 and 3 are valid roundings, in my case perhaps we would see the average of the 3 measurements as 4, but neither 3 nor 5 are close enough rounding?

Thus Beis Din might say that 3 and 5 are simply wrong, and too far off to be trusted, and we cannot join either of them with 4?

Perhaps we even have a principle that we believe 3 and 5 enough to give 4 more weight than just his own testimony, and we declare the new month, but we don't trust them enough to count them as full witnesses in this case?

Is there any record of anyone addressing this problem and its ramifications?

Chaim Chesler