SdpFinite

Li et al.'s composable finite key over the four-sequence record

8/8 passed in 2ms

Test	What it does	Result
test_interval_reduces	Li's expanded estimator with its interval collapsed onto the observed gains equals Gao's grouped one to 1e-14 at every pinned operating point.	✅ pass
test_interval_widens	The interval bound sits above the exact one at every block size and falls toward it, within 0.2% at 1e13 rounds.	✅ pass
test_kato_beats_azuma	Kato's deviation never exceeds Azuma's, equals it at half the rounds, and beats it 5x, 158x and 3353x as the count falls toward the dark-count floor.	✅ pass
test_kato_directions	The two Kato directions differ, the upper larger below half the rounds and smaller above, and both widen as the failure probability tightens.	✅ pass
test_length_below_rate	The finite key reaches 0.9852, 0.9624 and 0.9052 of the asymptotic rate at the three pinned operating points at a 1e11-round block, the shortfall growing with distance.	✅ pass
test_length_budget	Halving eps_sec costs exactly two bits and halving eps_cor exactly one, the length is a whole number of bits, and a phase error at the abort leaves nothing to hash.	✅ pass
test_length_converges	The length per round rises toward the asymptotic rate with the block, from 5.2% of it at 1e8 rounds to 99.6% at 1e13, never reaching it.	✅ pass
test_length_reach	The finite key distils at 40 km and is zero at 95 and 110 km, where the asymptotic bound has also stopped.	✅ pass