Global PCL-indexability of discounted single-project problems

Let $p_{01}$, $\rho$, $\kappa$, and $\beta$ be parameters satisfying

$$0<p_{01}<1,\qquad 0<\rho<1-p_{01},\qquad 0<\kappa<1,\qquad 0<\beta<1.$$

A discounted single-project problem is PCL-indexable when the conditions $\textup{(PCLI1)--(PCLI3)}$ hold on the full threshold range. Global PCL-indexability. For every feasible parameter tuple satisfying the displayed inequalities, the discounted single-project problem is PCL-indexable.

The conjecture extends the analytically tractable PCL-indexability results to the unresolved intermediate threshold regime. Numerical experiments found no counterexamples on extensive parameter grids, but a complete analytical verification remains open.