What does this equation mean?

Then do the one thing neither real-world case above allows: decommission the teacher . Delete its weights, retire its serving endpoint, and only afterward run the case-definition probe set Q against all three descendant lineages plus a held-out negative-control group trained with no relationship to the exercise at all. Compute I(m) for every model, $I_0$ from the negative controls, and $T_V$ , $T_H$ from the two exposed lineages; compute $\mu_V$ and $\mu_H$ from the surface form of every trait-positive response, and, if a curation step separates the teacher’s raw outputs from what the horizontal lineage actually trained on, compute s across that step. Because the trait was seeded rather than found, and because the teacher no longer exists to be queried, any trait that shows up in a descendant afterward has only one place it could have come from: whichever channel that lineage was assigned before the teacher was killed. Neither the R1 case, where the channel is disclosed and the teacher is alive and cooperating, nor the DeepSeek V3 case, where the channel is contested and the teacher’s own maker is unwilling to publish evidence, can offer that. Only a controlled trial can answer whether a specific behavior survives the specific death of the system that produced it.