DmcsCertified

The proved bound: what it may not exceed, and how much reach it buys

6/6 passed in 84088ms

Test	What it does	Result
test_beats_analytic	At 60 km and $\xi =0.01$ dm_rate is negative and dm_secure certifies key.	✅ pass
test_below_step_one	The certified bound stays under the Frank-Wolfe value it linearises about from 0 to 80 km and under the repeaterless capacity $-{\log }_2(1-\eta )$ to 120 km, and one Frank-Wolfe step certifies less than fifteen with both still under step 1.	✅ pass
test_cost_is_charged	dm_cost's p_pass and delta_ec equal the certified run's bit-for-bit, delta_ec is LUL19 Sec. IV D's $(1-\beta )H(Z)+\beta H(Z|X)$ at every $\beta$, and with no cut p_pass plus the dropped weight is one, an identity internal to the engine and not a published number.	✅ pass
test_cutoff_settles	From nc = 4 to 8 the step-1 objective moves under 2%, the certificate stays within 20% of it and the constraint violation under 1e-4, which sizes the cutoff assumption rather than removing it.	✅ pass
test_falls_with_loss	The certified rate falls monotonically with fibre length and with excess noise.	✅ pass
test_postselection_pays	At 80 km and $\xi =0.02$ a radial postselection cut lowers the pass probability and raises the certified rate, as LUL19 Sec. IV E reports.	✅ pass