Optimality of the 2n+3 winning-time bound

Establish whether, for every ncge4, every strategy of the first player admits a defense by the second player that survives to ply 2n+3, thereby proving that 2n+3 is the exact game length under optimal play.

Background

The paper constructs a first-player strategy that forces a win by ply 2n+3 for every ncge4, and exhaustive searches for n=4,5,6 find defenses that delay this particular strategy until that ply. These computations do not exclude the possibility that a different first-player strategy wins sooner. The unresolved problem is therefore to prove the corresponding general lower bound: for every first-player strategy, the second player should be able to survive until ply 2n+3. Together with the paper’s upper bound, this would establish the conjectured exact duration of the transversal achievement game under optimal play.