  The deformed Hermitian-Yang-Mills equation is a complex Hessian equation on
compact K\"ahler manifolds that corresponds to the special Lagrangian equation
in the context of the Strominger-Yau-Zaslow mirror symmetry. Recently, Chen
proved that the existence of the solution is equivalent to a uniform stability
condition in terms of holomorphic intersection numbers along test families. In
this paper, we establish an analogous stability result not involving a uniform
constant in accordance with a recent work on the $J$-equation by Song, which
makes further progress toward Collins-Jacob-Yau's original conjecture in the
supercritical phase case. In particular, we confirm this conjecture for
projective manifolds in the supercritical phase case.
