ReconcileEfficiency

Capacities, the three efficiency quantities and the published code tables

13/13 passed in 10ms

Test	What it does	Result
`test_asymptotic_table`	Published anchor: Jouguet Table I's 95.9%, 97.2% and 98.1% for the rate 0.1, 0.05 and 0.02 multi-edge codes, as R over the binary-input capacity at the quoted threshold.	✅ pass
`test_awgn_capacity`	`awgn_capacity` is $\frac{1}{2} \log_{2} (1 + SNR)$ , the I(A:B) of Leverrier arXiv:0712.3823 Sec. VI.	✅ pass
`test_biawgn_bounds`	The binary-input capacity sits under the Gaussian-input one, tending to 1 bit at high SNR and to the Gaussian-input value at low SNR.	✅ pass
`test_binary_anchor`	Published anchor: the rate-1/2 multi-edge code's 98.2% at s* = 1.074 is 0.9817 of the binary-input capacity and 0.9502 of the Gaussian-input one, so every published beta here is against the BIAWGNC.	✅ pass
`test_bridge_identity`	Published anchor: Martinez-Mateo Eq. (4) turns Table 3's f_EC column into its beta column in all twelve rows to 5e-5, the rounding of four printed decimals.	✅ pass
`test_charged_table`	Published anchor: Martinez-Mateo Eq. (6) turns Table 3's f_EC and frame error rate columns into its eta_EC column in all twelve rows to 3e-5.	✅ pass
`test_code_penalty`	A fixed-rate code's efficiency falls as SNR rises past its threshold, so the published beta is the largest it can claim.	✅ pass
`test_dimension_gain`	Efficiency rises with rotation dimension at every code rate, over the dimensions 1, 2, 4, 8 Leverrier's Theorem 1 allows.	✅ pass
`test_leak_ratio`	Eq. (5)'s leakage runs from 1 - R at no frame errors to the whole frame when every frame fails.	✅ pass
`test_pick_ladder`	`pick()` returns higher-rate codes as SNR rises, each decoding at that SNR.	✅ pass
`test_rotated_table`	Published anchor: all fifteen rows of Jouguet Tables II and III, block 2^20 at d = 0, 1, 2, 4 and 8, worst 0.0070 at rate 0.02, whose threshold is printed to two decimals.	✅ pass
`test_slice_comparison`	Consistency check, not an anchor: Leverrier's rate-0.26 code at SNR about 0.5 lands within 0.02 of the 90% he quotes, both given with "around".	✅ pass
`test_three_quantities`	At rate 0.8 over a BSC at 2%, f_EC is 1.41402 and beta 0.93180, on opposite sides of one.	✅ pass