After choosing the timing units, the construction of batches proceeds in the following way: for a given unit U, its batch index equals the lowest index k such that U is under the k-th timing unit.
This sounds similar to Main Chain Index in Byteball https://byteball.org/Byteball.pdf, odd that you didn’t mention Byteball in the first paragraph.
Anyway kudos for setting out to ground your research in the classical works. How could you extend it to networks without a finite set of participants (which is common in public networks)?
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