If you would like to learn more, check out the paper:

Let's consider the special case n=4, f=1, and for contradiction, suppose there is a protocol that has (f+1=2)-accountable safety under a delay-free network, but does not satisfy (f=1)-finality.

Thus, the difficulty is to show that accountability *even under synchrony* implies finality. For this, we prove that lack of f-finality implies lack of (f+1)-accountable safety in a delay-free network, which implies lack of (f+1)-accountability under synchrony.

Let's build some intuition why this result holds: If a protocol provides (f+1)-accountable-safety under partial synchrony, it trivially satisfies safety against f malicious replicas, a weaker property than accountability, under partial synchrony, i.e., f-finality.

The key Theorem 1 of our paper is then formally stated as

Now let’s dive into the technical details: Formally, f-finality means that the protocol retains safety under partial synchrony given f or less malicious validators.

... Also turn out to be implied by our result combined with impossibilities for safety and liveness under long-delay networks (formally, partial synchrony).

(ii) Impossibilities for accountable safety and liveness resiliences (Theorem B.1, "BFT Protocol Forensics" by @peiyaosheng @GaryWang523 @kartik1507 @sreeramkannan @viswanathpramod, ...

(i) Combined with the availability-finality dilemma (Theorem 3 of “Byzantine Generals in the Permissionless Setting” by @Tim_Roughgarden and @AndrewLewisPye , which rules out single-ledger protocols that satisfy both finality and dynamic availability...

Our result unifies earlier works:

What this says is that timing information does not help in accountable safety. Accountability under asynchrony is as strong as accountability under synchrony.

We show that if a blockchain provides any accountability (even in idealized delay-free networks), it also provides finality (safety under a long-delay network).

Finality means that the blockchain remains safe (no inconsistencies like double-spends) against many malicious validators, even when there are long network delays. 👇