Jup, the schemes are highly related. The way I think about it is that MMRs, certificate transparency logs and hypercore are essentially doing the same thing in slight variations: entry
n has a couple of disjoint trees of descending size in its past (take the binary representation of
n, each one-digit at position
k corresponds to a tree of size
2^k). The mechanism by which you connect those trees is almost an implementation detail. The optimally efficient accountable time-stamping has the earliest occurrence of that pattern I know about.
Bamboo uses the scheme from New Linking Schemes for Digital Time-
Stamping, whereas the analogy you described works even better for the scheme from Time-
Stamping with Binary Linking Schemes (which is exactly the log-2 construction you mentioned). I've been meaning to publish on this for a while, but writing takes so much time (as does teaching)...
I've been meaning to publish on this for a while, [...].
To specify that a bit: if you take the base-2 linking scheme construction but only store data in the leaves, you get a more efficient result than any prior published work. That construction is imo what the "optimally efficient accountable time-stamping" should have chosen, but apparently they didn't see it.
That construction is also highly related to a perfect deterministic skip list where the links between layers go into the "wrong" direction compared to a classic skip list: change the links that in the classic construction to always go to the highest possible layer, and you again obtain the base-2 linking scheme with data stored in leaves only.