Abstract: Consider the anti-self-dual equation over the product of the real line and a three-manifold with cylindrical end, with gauge group being SO(3). I will explain the proof of a Gromov--Uhlenbeck type compactness result for this equation. This is the first step towards constructing a natural bounding cochain for the symplectic side of the SO(3) Atiyah--Floer conjecture.