The generic $s=3$ lower-bound conjecture for spherical Einstein–Maxwell–scalar field evolution

Consider spherically symmetric admissible Cauchy initial data with non-vanishing charge and compactly supported initial scalar field, and let their maximal globally hyperbolic future developments have event horizons. Let the lower bound referred to in the source be the one in the stated interior instability theorem, with parameter $s$. Generic $s=3$ lower-bound conjecture. There exists a generic set of spherically symmetric admissible Cauchy initial data with non-vanishing charge and compactly supported initial scalar field such that the lower bound in the interior instability theorem holds with $s=3$ on each of the event horizons in the maximal globally hyperbolic future developments. This conjecture is motivated by lower bounds known for the linear wave equation on fixed subextremal Reissner–Nordström backgrounds and would support the nonlinear $C^2$ strong cosmic censorship result in spherical symmetry. The source does not establish the conjectured generic lower bound.