The area-threshold conjecture for counter braids

For a counter-braid ensemble, let $\bar{\epsilon}$ denote the area threshold, namely the value at which the area under the relevant extended belief-propagation extrinsic information transfer curve vanishes. The area-threshold conjecture asserts that

$$\bar{\epsilon}=\epsilon_{\mathrm{Maxwell}},$$

where $\epsilon_{\mathrm{Maxwell}}$ is the Maxwell decoding threshold; consequently, $\bar{\epsilon}$ is a lower bound on the maximum a posteriori (MAP) decoding threshold. The claim is motivated by the theorem establishing that the area under the expected residual graph's extended belief-propagation curve is zero at the area threshold, together with simulations and an asymptotic analysis of the Maxwell decoder; its resolution is not given in the source.