Positive-double-circuit conjecture for cosimple gammoids

Let $M$ be a cosimple gammoid of corank at least two. A positive double circuit is a double circuit whose circuit partition has more singular classes than multiple classes. Positive-double-circuit conjecture for cosimple gammoids. $M$ has a positive double circuit. This is presented as equivalent to the positive-coline conjecture under matroid duality, since gammoids are closed under duality and positive colines correspond to positive double circuits. Consequently, it is refuted together with the equivalent positive-coline conjecture.