Iterative roots of exclusive multifunctions

The candidate’s solution correctly reconstructs and justifies the paper’s increasing-case construction on I\J(F) (via conjugacy from the absorbing interval), and its extensions at jumps for cases (J1) and (J2), as well as the nonexistence bound in case (J3). These align with Theorems 3.1–3.4 of the paper. However, the “optional (decreasing roots)” part is incorrect/incomplete: for the decreasing square-root case at a jump in (J2) the paper requires a two-sided definition at ci and the extra condition J(F) ∩ (lim_{x→ci+} f∗(x), lim_{x→ci−} f∗(x)) = {ci}; the candidate omits this condition and uses a one-sided interval [lim_{s→ci−} f∗(s), ci], which in general does not yield f^2 = F, contradicting Theorem 4.3.