Resolution criteria
This market resolves to YES if, by December 31, 2029, 23:59:59 UTC, either of the following conditions is met:
Discovery: A specific integer triple $(a, b, c)$ is identified and publicly verified to form a perfect Euler brick (satisfying $a^2 + b^2 = d^2$, $a^2 + c^2 = e^2$, $b^2 + c^2 = f^2$, and $a^2 + b^2 + c^2 = g^2$ for positive integers $a, b, c, d, e, f, g$). Verification requires that the calculation can be checked directly and is acknowledged by established mathematical repositories (such as MathWorld, OEIS, or peer-reviewed literature).
Proof of Non-existence: A mathematical proof demonstrating the non-existence of a perfect Euler brick is published in a peer-reviewed academic mathematics journal or broadly accepted as sound by the mainstream number theory community (e.g., through formalization in a proof assistant like Lean or general consensus following an arXiv preprint).
If by the end of 2029 the existence of a perfect Euler brick remains an open problem with no verified example and no widely accepted proof of impossibility, the market resolves to NO.
1,000