DmcsBudget

The finite-size pieces that ship: the dimension price, the energy test and the length

16/16 passed in 2ms

Test	What it does	Result
test_accept_halves	Theorem 4's acceptance half-width is Hoeffding's, the semidefinite form exactly half the general one, and it narrows as one over the square root of the rounds.	✅ pass
test_energy_domain	dm_energy refuses $l_T/k_T\ge w/r$, where Theorem 3 does not hold, $l_T\ge k_T$, and a radius leaving the incomplete gamma outside f64.	✅ pass
test_energy_formula	The returned logarithm is Eq. (5), ${\log }_2(l_T+1)$ minus $k_T$ times the Bernoulli Kullback-Leibler divergence in bits between the observed and claimed failure fractions.	✅ pass
test_energy_ratio	Theorem 3's $r$ is one over the regularised upper incomplete gamma to 1e-11 against the Poisson tail identity, and never below one.	✅ pass
test_energy_trade	More test rounds and a larger claimed weight each lower the energy-test failure probability, while Eq. (4) charges the larger weight back (Kanitschar Sec. VI B).	✅ pass
test_length_approaches	At fixed keying fraction and leakage share the rate per signal rises with the block and converges from below on the entropy less leakage and dimension charge, to 1e-4 at ${10}^{14}$.	✅ pass
test_length_assembles	dm_length returns Theorem 6 Eq. (9) in bits over the block, rebuilt here from the equipartition and dimension terms the same call returns, and floors only the reported length.	✅ pass
test_length_guards	dm_length refuses an entropy above ${\log }_2|Z|$ and keyed rounds above n_total, and dm_price a one-symbol key map.	✅ pass
test_length_source	dm_length refuses an entropy from the asymptotic feasible set, whose minimum overstates the key since that set is contained in the relaxed one, and an unknown source.	✅ pass
test_price_dominates	At a weight of 1e-4 and ${10}^{12}$ signals the dimension-reduction charge, 0.101 bit per pulse, exceeds the equipartition correction by over three orders.	✅ pass
test_price_form	dm_price equals Kanitschar Eq. (4) evaluated here across five weights and four key-map sizes, and is exactly zero at zero weight.	✅ pass
test_price_quoted	dm_price gives the 0.101 and 1.34e-2 bit the certified refusal quotes and rises with both the weight and the key-map size.	✅ pass
test_secpar_branches	Each of the two maximised branches, privacy amplification and testing, can bind the composed parameter.	✅ pass
test_secpar_shape	Kanitschar's five demonstration epsilons compose to their stated 1e-10 through a correctness term outside a maximum over two branches, which a plain sum overstates and a plain maximum understates.	✅ pass
test_weight_falls	More test rounds buy a smaller weight and a smaller dimension-reduction charge at a fixed failure probability, and a positive target logarithm is refused.	✅ pass
test_weight_inverts	dm_wchoice's $w_{ϵ}$ (Sec. VI B) inverts Eq. (5): fed back to the energy test it returns the target logarithm to 1e-6.	✅ pass