# Let D be delay diameter of the network ,All the blocks will be either adopted or abondoned by all nodes at t+3D in the GHOST protocol?

I have read GHOST white paper some time. and some problems abount Proposition 2(The Convergence of History) in Chapter 5.1 is confused to me.Does it imply that all the blocks will be either adopted or abondoned by all nodes at t+3D? Assume here is a blocktree rooted by A and its left child and right child is B and C respectively,at time t a block D whose parenet is B is genereated,then according the GHOST rule,A B D will be the main chain. Assume at time t+d,the block E whose parent is C is generated, then what's the main chain of this block tree?

By t+D all nodes in the network will know that ABD is the main chain (i.e. blocks B and D will be adopted and C will be abandoned) since D is delay diameter of the network, which is a maximum propagation delay in the network. The paper says that block E should be created between t+D and t+2D. Let's assume that the interval is left-open, that is that E is created at t_E such that `t+D < t_E <= t+2D`. By t+3D all nodes will know about E but will abandon it because ABD was seen sooner than ACE. So by t+3D E will be abandoned and ABD will be the main chain.
I honestly don't know what could happen if `t+D == t_E`. I'm also struggling with the paper, so please correct me where I'm wrong.