DpsFinite

Phase 9: MTT23 finite-key DPS length, and the receiver it refuses

17/17 passed in 2174ms

Test	What it does	Result
test_azuma_loses_reach	Replacing Kato by Azuma costs the whole key at $\eta =0.1$, the divergence the paper's Fig. 5 reports.	✅ pass
test_domain_guards	Every argument of dps_phase is refused by name outside its own domain.	✅ pass
test_empty_run_refused	A run that detected nothing is refused rather than reported as a zero phase error.	✅ pass
test_epsilon_composition	The paper's own ${\zeta }^{\prime }=28$, $\zeta =58$ and ${ϵ}_1={ϵ}_2=2^{-58}/6$ compose to exactly $2^{-27}$ under its Eq. (50).	✅ pass
test_kato_beats_azuma	The Kato branch of dps_phase returns a smaller phase-error bound than the Azuma branch at every point of an $\eta$ ladder.	✅ pass
test_kato_constraint_is_tight	The returned pair sits on Kato's constraint surface with equality, so the failure probability it is certified at is the one asked for.	✅ pass
test_kato_solves_its_problem	dps_kato returns the pair minimising Kato's deviation term subject to his failure-probability constraint, against a direct scan.	✅ pass
test_length_falls_with_error	The length falls as the sample-round bit error rate rises, clamping at zero rather than going negative.	✅ pass
test_length_rises_with_block	The length per emitted pulse rises with $N_{em}$ at a fixed operating point.	✅ pass
test_optimal_intensity	The length peaks at the mean photon numbers the paper's Sec. V prints, 9.3e-3 at $\eta =1$ and 9.4e-4 at $\eta =0.1$, to its two figures.	✅ pass
test_prediction_below_half	Kato's prediction must sit below half the trials, which is the condition his analytic optimum is solved under.	✅ pass
test_reach_falls_short	At the paper's 77 km the shipped length is 1.12 Mbit where its own text claims 3 Mbit, and 3 Mbit is reached at 73.4 km instead.	✅ pass
test_source_tail_is_exact	dps_source matches a 60-digit evaluation of Eq. (51) to twelve digits at mean photon numbers spanning eight decades.	✅ pass
test_source_tail_is_ordered	$q_1\ge q_2\ge q_3$: the bounds fall with the photon number they count from, because Eq. (3) reads each as a tail, not a weight.	✅ pass
test_tail_order_enforced	Source bounds handed over out of order are refused, because reading them as three independent weights would understate the phase error.	✅ pass
test_threshold_receiver_refused	A threshold receiver is refused by name, and the message enumerates what a click record cannot supply.	✅ pass
test_unknown_receiver_refused	A receiver name other than the two the engine knows is refused rather than silently treated as resolving.	✅ pass