PoEM more accurately measures work.   Proof-of-Work limits how "heavy" a block can be, treating all blocks that exceed the difficulty threshold as equal.   PoEM weighs blocks beyond the difficulty threshold, to ensure that even if two valid blocks are proposed simultaneously, one will always be "heavier" than the other.   With this change, the way total difficulty is measured also changes. Proof-of-Work uses a linear growth of total difficulty (additive) while Proof-of-Entropy-Minima uses an exponential growth of total entropy (multiplicative).  The result  no consensus based forks & faster finality, which both act as prerequisites for the ability to coordinate an infinite number of execution shards. 

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