Equiconsistency conjecture for indestructible weakly compact cardinals

Let $ZFC$ denote Zermelo–Fraenkel set theory with the axiom of choice. A cardinal is indestructibly weakly compact if its weak compactness is preserved by the relevant forcing described in the paper.

Equiconsistency conjecture. The existence of an indestructible weakly compact cardinal is equiconsistent over $ZFC$ with the existence of a supercompact cardinal.

The paper's main theorem rules out a Laver-like preparation making a weakly compact non-supercompact cardinal indestructible, but does not establish the full consistency-strength equivalence. The conjecture is motivated by the reported high consistency strength of indestructible weak compactness and remains open here.