Tree reconstruction asks whether observations far from the root retain information about a random root state transmitted through noisy independent edge channels. In the four-state ferromagnetic channel, the root is uniform on four states and a child has conditional transition probability
 |
where 
and 
is the Kronecker delta. Different children are
independent conditional on their parent's state. Reconstruction occurs if the expected
total variation distance of the root posterior,
conditional on depth-
spins, from the uniform
distribution has a positive limit as 
.
