There is now formal security proof showing the safety and liveness of Proof-of-Entropy-Minima (PoEM).  https://eprint.iacr.org/2024/200

This relatively simple adjustment to the measurement of block weight has been empirically shown to: prevent selfish mining, create faster finalization time, increase throughput, and decrease block times while maintaining safety and liveness of the chain.  Modifications to the current heaviest chain rule are very straight forward.

The TL;DR is:

Presently the heaviest chain rule does not treat blocks as being dependent events even though they are dependent because of the hash link to the parent.

PoEM uses combinatorics to weigh the dependent block events appropriately. This generates a guaranteed unique weight for each block which is the average number of hashes, in expectation, that would be required to produce a chain of equal weight.

The guaranteed unique weight prevents the network from mining on competing forks because the likelyhood of having blocks of equal weight is (1/2^256) ~= 0

Additionally, the process naturally introduces randomization on each sample (ie block) which prevents profitable withholding attacks.

Finally, it shows that the threshold for a Sybil attack can be improved from 33% to 40%.