In other words, if our 3.8 billion + has been fully documented by the firm KRY hired to do this exercise and the ICSID doesn't disagree with the amount, would the tribunal typically rule in accordance . . .

Yes, EZ, sort of. :) The BIT is the law for the arbitral panel and it is a mandatory statement: shall. They will look at the arguments from both sides as to what that amount should be, assuming liability, which I personally think is clear and not open to a strong defense.

That said, arbitrators often "split the baby." So they could come up with any amount between the actual costs incurred of $500 million and the requested $3.8 billion, assuming we have a rational argument for that being the "genuine value." The award of interest is also mandatory at the "normal commercial rate."