The even-rank conjecture for CRIM positions

A partition is a Young diagram, and its rank is the relevant rank statistic on the partition used in the CRIM analysis; a position is a $\mathcal P$-position when the next player loses. Even-rank conjecture. Every $\mathcal P$-position has even rank. Computations and the listed families establish even rank as a necessary condition in many cases, but the conjecture is intended to cover all partitions and remains unresolved in the source.