Explanation of the unexplained K=8 composition residuals

Determine why all five K=8 language-model ecosystem arms exhibit positive residuals relative to the fitted relationship between pool travel propensity and five-generation collapse drift.

Background

The paper proposes a travel-propensity index based on how readily the contributing models are carried along by recursive training. Across nineteen experimental arms, this index explains substantial variation in five-generation drift, but more than thirty percent of the variance remains unexplained.

The unexplained residuals are systematically positive for all five K=8 arms, indicating an ecosystem-size-specific deviation rather than ordinary seed noise. The authors explicitly state that they do not know the cause of this pattern, leaving its mechanism unresolved.

References

Five arms agreeing is not one arm's jitter; the index misses something about $K{=}8$, and we do not know what.

The Oligarch Barely Steers Model Collapse in Multi-Model Ecosystems  (2609.11146 - Liu et al., 10 Sep 2026) in Appendix, Section Composition Index Details