The Gog–Magog bijection conjecture

A Gog triangle of size $n$ is a triangular array satisfying the Gog-triangle conditions, and a Magog triangle of size $n$ is a triangular array satisfying the Magog-triangle conditions. An $(n,k)$ Gog trapezoid and an $(n,k)$ Magog trapezoid are the corresponding truncated triangles of size $n$ and parameter $k$.

Gog–Magog bijection conjecture. There exists a bijection from Gog triangles of size $n$ to Magog triangles of size $n$, which maps $(n,k)$ Gog trapezoids to $(n,k)$ Magog trapezoids for all $k\leq n$.

This conjecture seeks a bijective explanation of the equality between the enumerations of Gog and Magog triangles while preserving the natural trapezoid subclasses. The source does not state a resolution, so the conjecture is recorded as open.