Recent 12-marker DNA test results of a Wilhelm Adam Woolf descendant match test results of two William Wolf descendants.

That proves we're related, but does it prove Gottlieb was William's father?

As much as we would like for the results to be proof that Gottlieb was William's father, the DNA results only provide a probability of "Most Recent Common Ancestor". The DNA tests we've been getting don't indicate paternity, but rather a probability that we're related within a certain number of generations.

For example, the Family Tree DNA site gives the probabilities as:

Probability

The current, 12-marker results indicate only a 50% probability that our common ancestor was within the past 7 generations, as would be the case if Gottlieb was William's father. Identical 37-marker results would raise the probability to 90% probabillity that our common ancestor was within 5 generations and to 95% within 7 generations.

That still won't identify William's father. But, it will at least help us better direct our efforts for finding documentation that does.