Steady-soliton limit conjecture for pluriclosed flow on Class VII+ surfaces

Let $(M^4,J)$ be a compact Class $\mathrm{VII}_+$ surface, let $\omega_0$ be a pluriclosed metric on $M$, and let $p\in M$ be a generic point as described in the surrounding discussion. Class VII+ soliton-limit conjecture. The solution $\omega_t$ exists on $[0,\infty)$, and the pointed spaces $(M,J,\omega_t,p)$ converge in the pointed $C^{\infty}$ Cheeger–Gromov sense to a nonflat complete steady soliton $(M_\infty,J_\infty,\omega_\infty,p)$ with smooth function $f_\infty$, such that $\theta^{\sharp}_\infty+\nabla f_\infty$ is $J_\infty$-holomorphic, $M_\infty$ compactifies to $(\overline M_\infty,\overline J_\infty)$, and the orthogonal distribution is integrable with generic leaf whose closure is a global spherical shell. The passage presents this as a conjectural summary and gives no resolution.