Test the target-register explanation for model-dependent hypothesis behavior

Determine whether differences in models’ standing-hypothesis behavior arise from the relative nativeness or register cost of expressing the hypothesis in the target framing.

Background

The appendix discusses a possible explanation for why models retain a field hypothesis when translating into vector-space prose but often omit it when translating into module-theory prose. The proposed account is that models trade off mathematical requirements against the linguistic naturalness of the target framing: target-native expressions such as “In Set” may be favored, whereas importing an explicit field assumption into module-theoretic prose may be disfavored.

The authors report that two models agree on item-level outcomes and that the available evidence is consistent with this explanation, but explicitly state that the three framing pairs in the corpus are insufficient to test it. A broader corpus of framing pairs would be needed to resolve the hypothesis.

References

Two models weighting that trade-off differently would produce exactly the observed inversion. We record this as a hypothesis; three framing pairs cannot test it (§5).

— Objects Without Morphisms: What LLMs for Mathematics Do Not Represent  (2610.03551 - Wang et al., 2 Oct 2026) in Appendix E.3, “Why M1’s directional index is negative: four explanations, two excluded”