If Proof school ever officially completes against the Nueva US (as in a direct face-off) in any competitive "sport" (such as, a school vs school chess, debate, volleyball, etc.), this will resolve depending on the winner (in case of a tie, that particular face-off is disregarded).
If such an event happens with acceptable criteria, this market will resolve to the victor.
Clarifications and specifications: (long)
A face-off against unofficial representatives does not count. For instance, a proofnik facing against a maverick in tennis singles will only count if 1) this match is in a competition 2) each member represents their school's competitive team and 3) each member is the only member of the schools team. If there are multiple members, overall ranking is what determines the outcome (in which case #3 is disregarded)
Academic tests are almost always not going to meet the criteria. For example, if both a Proof and Nueva team are competing in NACLO, since the schools never directly "face-off" and instead participate in a larger test, this will not meet the criteria. However, academics such as debate may only meet the criteria if the teams directly face each other.
School-hosted competitions are fair game. If Nueva hosts an archery competition, and there is an official Nueva team, an official team sent by Proof are valid grounds to resolve this.
Resolution will generally follow these guidelines, with ambiguities decided on a case by case basis.
Note: the "US" stands for upper school, as in high school. This is made to ensure competitors of roughly the same age (Nueva is K-12)
Related questions
@zweezwee I'm not familiar with robotics. Do two robots directly compete against each other? Or are points measured for each robot independently?
@KyleWan there's no direct competition since every match is played with three teams per side (for frc at least), but there are tournament rankings
@DeadRhino yes, in the sense that it would be clear from the match who won, but this can be a single or a few games in a larger tournament, for example. (In which case Proof or Nueva won't be the winner of the tournament, but may place above the other)
Such an example is a math madness face-off, which counts as long as the Nueva team and Proof team are paired against each other for at least one match.