So we have 3 assumptions:
1. We can identify work done for Bitcoin
2. We can communicate with other participants
3. Attacker doesn't have too much hashing power
Is it enough?
point 1 isnt an assumption as it is proven through mathematics (in case you think its an assumption please add that 1+1=2 keeps true as well - it is also needed

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we will always need some kind of calculator: humans are just too slow
bandwidth and latency is also interesting as it defines bitcoins upper bound