DmcsShape

Penalty growing with distance and the small, shrinking optimal modulation

3/3 passed in 81ms

Test	What it does	Result
test_alpha_penalty	Past the optimum the QPSK key falls monotonically with $\alpha$ and is negative by $\alpha =0.7$ at 20 km, $\xi =0.01$, where the Gaussian rate still climbs.	✅ pass
test_gap_widens	At $\alpha =0.4$, $\xi =0.005$ the QPSK rate falls monotonically from 49.9% of the Gaussian rate at the transmitter to 13.9% at 50 km.	✅ pass
test_optimal_small	The optimal QPSK $V_A$ falls from 0.538 to 0.166 SNU over 0 to 80 km, where Gaussian modulation wants $V_A$ above 5 at 40 km.	✅ pass