This paper studies resonant and Jordan derivative-order ladders of solutions, establishing that the ladder sequence satisfies a unique minimal annihilator polynomial. We derive constant-coefficient closures of these ladders, proving that the entire derivative-order sequence can be recovered from a finite window of values. We characterise resonant periodicity and Jordan obstructions to full recovery, providing a complete classification of periodic and resonant cases. The results yield explicit finite-window exact recovery laws for derivative-order ladders and reveal the structure of minimal annihilators and closure relations.
Mohammad Abu-Ghuwaleh (Tue,) studied this question.