ProtocolDiscrete

Phase 5c API: phase-shift keying and the correlation a finite alphabet cedes

13/13 passed in 20442ms

Test	What it does	Result
test_bits_is_required	dm_holevo requires the alphabet entropy, holevo() passes log2(m), and the capped value is at most the unbounded one.	✅ pass
test_both_informations	Both informations are reported and beta*gauss - chi_BE rebuilds the published rate, the gap under 1% at the operating point and over 10% at a bright eight-state ring.	✅ pass
test_certified_reach	The numerical proof certifies key where the closed form is negative, and the report carries both numbers side by side.	✅ pass
test_constellation	constellation() is states amplitudes of modulus alpha equally spaced from the real axis, as _core.dm_states returns them.	✅ pass
test_discrete_costs	z_star sits below the Gaussian value, the rate below the Gaussian-modulation rate at the same variance, and the gap closes as states are added.	✅ pass
test_effective_plane	z_star, i_ab and chi_be rebuild bit for bit from the reported T_eff and xi_eff alone.	✅ pass
test_engine_agreement	The rate is exactly _core.dm_rate and the reported mutual information dm_info's at the effective channel, pinning the untrusted substitution T -> etaT, xi -> xi + 2v_el/(eta*T).	✅ pass
test_guards	The closed form refuses a trusted receiver, a homodyne and a finite block, and a two-state constellation is refused at construction.	✅ pass
test_information_wrapper	information(T, xi) returns (exact, Gaussian) = (0.1107575, 0.1107648), bit for bit _core.dm_info(4, 0.4, 0.5, 0.01), transposed slots give 0.0023007, and domain errors reach the caller; tree values, not a published anchor.	✅ pass
test_steps_apart	bound is step 2 and is the proof, upper step 1's Frank-Wolfe value labelled a diagnostic, and the certificate refuses a key_rate; before a run those rows and the solver read unrun.	✅ pass
test_trusted_plane	A trusted receiver reaches _core.dm_trusted at the channel plane with efficiency and electronic noise held apart, never folded into the transmittance.	✅ pass
test_trusted_reach	The untrusted branch refers v_el back as xi + 2v_el/(etaT) and certifies nothing at T = 0.5, 0.2 or 0.05, where the trusted one certifies key at all three.	✅ pass
test_trusted_rows	The trusted report drops T_eff, xi_eff, key_analytic and key_gauss and returns i_ab and chi_be as None, keeping the claimed plane, the trusted flag and the certificate's rows.	✅ pass