摘要：

        In this work, we establish compactness and regularity results for complete gradient Laplacian solitons of closed G₂-structures. Under a lower scalar-curvature bound and a distance dependent bound on the soliton potential, we prove pointed measured Gromov-Hausdorff compactness. With a uniform lower bound for the localised Perelman entropy, the Gromov-Hausdorff convergence improves to pointed C^1,a convergence. We then establish G₂-specific differential identities and quantitative interior estimates showing that local bounds for the Riemann curvature control the full soliton data, including the positive 3-form, the torsion tensor, and the potential function. As applications, we utilise the properties of the localised Perelman entropy, to prove an entropy epsilon-regularity theorem, a gap theorem for scalar-flat solitons, and smooth convergence of the G₂-structures on the regular set. Finally, at the critical exponent in dimension seven, we show that a uniform weighted L^7/2 curvature bound then yields pointed C^∞ compactness.