The symplectic connected-sum conjecture for simply connected four-manifolds

A smooth, closed, oriented and simply connected $4$-manifold is a smooth manifold of dimension four with the stated properties. A symplectic manifold is a smooth manifold equipped with a symplectic form, and a connected sum is formed by deleting balls and gluing along the resulting $3$-sphere boundaries. The symplectic connected-sum conjecture. Every smooth, closed, oriented and simply connected $4$-manifold is the connected sum of symplectic manifolds, with both the symplectic and the opposite orientations allowed. This ambitious claim would imply the smooth Poincaré conjecture, but the source explicitly states that it remains open; it is refuted only after enlarging the class of manifolds beyond the simply connected case.