What does this equation mean?

A trait needs a case definition : an automatable rubric, applied to a fixed, held-out probe set Q never seen during any training run under discussion, that scores each response as trait-positive or trait-negative without a human arbitrating every case. For the self-identification trait, a workable case definition might require a named-entity match against a disallowed-parent list across a fixed battery of “who built you” phrasings, with paraphrase and translation variants included to block trivial gaming. For a reasoning-style trait, it might require a specific rare token sequence or a specific verify-then-restart pattern in a chain-of-thought transcript, chosen because two teams solving the same problem independently would be unlikely to reinvent it. The case definition is the whole experiment’s foundation: a trait defined loosely enough to include ordinary competence will show “transmission” everywhere, and one defined so narrowly that only a byte-for-byte copy counts will show it nowhere. Every later claim inherits whatever the case definition gets wrong.