  In a close look at the replica wormhole derivation of the island conjecture,
we note a discrepancy in the derived matrix eigenvalues in the limit where the
Hawking radiation entropy goes to zero. The small corrections to the density
matrix for the radiation infer that ${\rm tr}(\rho_\textsf{R}^2)$, equally a
sum over the eigenvalues squared, must be small ($\ll1$) at all times. This is
in contradiction with an ensemble dominated by a density matrix with an
eigenvalue close to unity. Also, the radiation entropy has been approximated by
the ensemble averaged entropy, as in a final state analysis. For
$\rho_\textsf{R}=\rho_\textsf{R}(\sigma)$ with $\sigma$ the set of variables
used in the average, the ensemble average is only an accurate estimate of the
entropy after $\sigma$ has been measured. At the formation of each Hawking
pair, there is a distribution over $\sigma$ that affects the entropy. Without a
real time determination of $\sigma$, the radiation entropy follows Hawking's
result during the evaporation. A question remains of how quickly such
determinations can be assumed to occur. A complete argument for that the
radiation entropy follows the Page curve should address this.
