Assess genuineness and significance of the p=3 d-type instanton instability

Ascertain, for the p = 3 truncated single-cut saddle that remains the only self-consistent single-cut solution where the dominant saddle ceases to exist, whether the observed d-type instanton condensation constitutes a genuine instability contributing to the original path-integral contour, and, if so, characterize the physical significance of this instability in the dual gravitational description.

Background

At truncation level p = 3, the authors observe an apparent instability on the subdominant single-cut saddle against condensation of d-type instantons, including in a charge range where this saddle is the only viable single-cut description in the microcanonical ensemble.

They caution that it is not established whether this is a genuine instability that contributes to the original contour without a Lefschetz thimble analysis, and they also leave open the question of the physical meaning of such an instability if confirmed.