This answer indicates that the US constitution requires that The President's salary may not increase or decrease throughout their term.
To me, this is ambiguous as inflation constantly diminishes the value of the compensation package.
As such, is it possible that a challenge of this article could result in the compensation being linked to inflation or is this settled by case law?
The term salary is unambiguous - it is the amount you are paid for the work that you do. The Constitution prohibits this amount from being changed during a President's term of office so it can only be adjusted at the transition from one term to the next. Congress could pass a law that this is an automatic adjustment in line with inflation (or anything else).
The Constitution says that
The President shall, at stated Times, receive for his Services, a Compensation, which shall neither be encreased nor diminished during the Period for which he shall have been elected, and he shall not receive within that Period any other Emolument from the United States, or any of them.
If the compensation, as enacted in law, is stated in a dollar amount as it is under 3 USC 102, then POTUS gets $400,000 per year, no more and no less.
Congress can write laws that refer to formulas, rather than a specific integer amount. Let's assume that they do this and pass a law where (during the period when that law holds i.e. the president's current term) the compensation is stated as the result of a computation of variable values (in particular, an inflation index).
Then somebody sues, and the Supreme Court has to decide whether the constitutional clause means that POTUS gets the same number of dollars throughout his term, or does it mean that Congress cannot change the law of computation during the term. On both sides, it's easy to declare that the meaning is clear. The question of original meaning would figure largely in that discussion. SCOTUS would have to discern what the intend of The Framers was – was it a belief that there is an intrinsic good behind limiting a president's compensation to a fixed number of dollars; or, is it intended to require that a change in the law which implements the presidential compensation, and the approval therein by POTUS, must itself be subject to a form of approval by the people (voting out the rascal who approved his own raise).
The issue has not previously come before the Supreme Court, so we don't have any precedent. Historical research into the origin of this clause would be important in determining what the original intention was. The most likely motivation for such a clause would be as a check on the boss setting his own compensation without checking that power, hence a formula-based compensation is reasonably related to a credible intent behind the clause. We can explain why The Framers did not directly address this interpretation, since it only comes up when there is a massive discrepancy between nominal dollars and real money as fixed units of gold, which at the time would have made no sense.
