SdpReach

Figure 1: what the exact worst case buys in rate and in distance

4/4 passed in 13717ms

Test	What it does	Result
test_abort_later	The analytic bound reaches the $E_p\ge 1/2$ abort between 110 and 125 km, where the certified one is still below it.	✅ pass
test_peaks_local	The pinned operating points are local maxima in both the intensity and the splitter.	✅ pass
test_rate_doubles	At each bound's rate optimum the certified rate is 2.087, 1.879 and 1.876 times the analytic one, Fig. 1(a)'s headline, falling as the square of the transmittance.	✅ pass
test_reach_extends	The certified rate survives 100 km on this exam's channel, where the analytic one is live at 90 km and gone by 95 km.	✅ pass