How does a vicious circle use a chain of claims to support itself?

A vicious circle, or circulus in probando, is a specific form of circular argument that utilizes a chain of claims to support itself. In this structure, a series of premises ($p_1,p_2,\dots ,p_n$) are linked together in a sequence where each premise is used to prove the next: $p_1$ proves $p_2$, $p_2$ proves $p_3$, and so on, until $p_{n-1}$ is used to prove $p_n$.1

The fallacy is completed when the final claim, $p_n$, is then used to provide evidence for the initial premise, $p_1$. By creating this closed loop, the entire series of claims is treated as established, even though the argument lacks independent proof and merely assumes the truth of its own conclusion. Because no one who questions the final conclusion could logically concede the initial premise, this method fails to provide genuine reasoning or power of conviction.1