I’ve read up on Babson tasks, and they mention that all known tasks are not perfect because there are duals. I’m not sure what this means exactly. What precisely is a “dual” in chess problems?
A dual is an alternate solution, other than the intended one, after the first move of a problem or study. If it happens on the first move, the problem or study is called cooked instead.
Ideally, White should have only one move at each juncture that solves a problem. If White has an alternative at any stage other than the first move, this is a dual. A dual is not as serious a flaw as a cook, and in minor lines, duals may be permissible (opinions differ on this point). Some problems make a virtue out of dual avoidance – of two apparently equivalent white moves, only one works.