The class IP

The class $\mathrm{I}\mathrm{P}$ consists of languages having an interactive protocol with a probabilistic polynomial-time verifier and polynomially bounded interaction as in Interactive-proof transcripts, rounds, and prover strategies, completeness at least $2\mathrm{/}3$, and soundness at most $1\mathrm{/}3$ in the sense of Completeness and soundness of an interactive protocol.

Replacing these two constants by any fixed $c,s$ with $0<s<c<1$ defines the same class. To see this from a $(c,s)$ protocol, choose a dyadic rational $a$ strictly between $1\mathrm{/}2-c\mathrm{/}4$ and $1\mathrm{/}2-s\mathrm{/}4$. After the original protocol, use fresh private bits to accept with probability $a+1\mathrm{/}4$ if its decision was acceptance, and with probability $a$ otherwise. Both probabilities are dyadic numbers in $[0,1]$, so a fixed finite number of fair bits realizes this rule exactly. The new completeness is at least $a+c\mathrm{/}4>1\mathrm{/}2$ and soundness at most $a+s\mathrm{/}4<1\mathrm{/}2$. Apply Sequential repetition amplifies completeness and soundness gaps with $\epsilon =1\mathrm{/}3$ to obtain the defining IP constants. Conversely, starting from the defining constants, apply the same lemma with $0<\epsilon \le \min \{1-c,s\}$ to obtain completeness at least $c$ and soundness at most $s$. All added randomness and repetitions have bounds constant in the input length. No endpoint assertion about zero soundness or perfect completeness is included in this constant-gap argument.