This paper delves into the fundamental trade-off between security, latency, and throughput in proof-of-work longest-chain-wins protocols, also known as the Nakamoto consensus. New upper and lower bounds on the probability of violating transaction safety are derived as a function of honest and adversarial mining rates, an upper bound on block propagation delays, and transaction confirmation latency, both in time and in block depth. The results include a first closed-form finite-latency bound applicable to all delays and mining rates up to the ultimate fault tolerance. Notably, for most parameters relevant to Bitcoin and proof-of-work Ethereum, the gap between the upper and lower bounds is significantly narrower than the best gaps previously established in the literature. Furthermore, the paper reveals a fundamental trade-off between transaction throughput and confirmation latency, ultimately determined by the desired fault tolerance and the growth of block propagation delay as block size increases.

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