Daykin–Häggkvist conjecture on completing dense partial Latin squares

Let $P$ be an $n\times n$ partial Latin square in which each symbol, row, and column contains at most $\frac{1}{4}n$ nonblank cells. Daykin–Häggkvist conjecture. Every such partial Latin square can be completed to a Latin square. This is a central completion problem for partial Latin squares and is linked to Nash-Williams's conjecture on triangle decompositions; the source does not provide evidence of resolution.