The imported approximate conversion

Validated upper bounds on $e$ or $r_{\mathrm{dec}}$ may replace their exact values. A finite decoder certificate must establish CPTP feasibility, not merely a favorable objective value. For a decoder with input dimension $D_R$, its normalized Choi conditions are

The factor $d$ in the logical Choi conversion is not omitted. The regulator allowance $b$ is already a half-diamond allowance and is not multiplied by $d$.