In multi-stage protocols, one script refers to the script of the next stage (example in script1, we have the statement hash(OUTPUTS(0).propositionBytes) == script2Hash).
But suppose we also want the script2 to refer back to script1, (example we want hash(OUTPUTS(0).propositionBytes) == script1Hash), then its a cyclic reference.
One solution is to store script1Hash in register of the box containing script2. Additionally script1 is modified to ensure that the corresponding register of any box containing script2 equals hash(SELF.propositionBytes).
EDIT: While the “vanilla” perpetual token is interesting, the more powerful one is the “max-once-per-block-use” perpetual token, which should be a separate design pattern.