Positivity of Single-Centred Black Hole Indices in the \( \mathbb{Z}_2 \) CHL Model

We prove Sen's positivity conjecture for single-centred quarter-BPS black holes of the \( Z_2 \) CHL model for every charge with \( Q^2\le2 \) and for every charge of discriminant at most 800. For all charges we reduce the conjecture to an explicit level-two Rademacher expansion of the dyon partition function and prove it under that hypothesis.