Why it is a question
THEORY-234, narrowed on 2026-10-19, holds two things for softmax next-token predictors on a shared vocabulary. Two models induce the same distribution exactly when they are extended-linearly equivalent (Theorem 5). And a relational linear property is shared by all such models or none when it lies in the subspaces that enter the logits: Γ ⊆ N, with Γ_q ⊆ M (Theorem 14). Both were re-derived for the promotion audit’s batch 012 (ADR-047). Until that date, THEORY-234’s promote_when also asked, as an alternative, for “a measurement in released language models of the subspaces M, N and Γ_q for relations where linearity has been reported, showing whether Theorem 14’s conditions hold there”. That asks whether the theorem bears on trained models, which THEORY-234 disclaims. It moved here unchanged.
It is open because every result in LIT-950 needs exact equality of distributions, and the paper has no experiments (NOTE-746). The record holds reports of linear relational structure in single trained models. Those say nothing about the equivalence class.
What would answer it
A measurement on one or more released models. Estimate F, G, M and N from the embeddings and pivoted unembeddings, then, for relations where linearity has been reported, estimate Γ and Γ_q and test Γ ⊆ N and Γ_q ⊆ M, with a tolerance stated in advance. It would show the reported properties to be properties of the distribution if the containments hold. It would show them to be possibly artefacts of one fitted model if Γ_q has a substantial component in F outside M. Further reports of linear structure in single models cannot settle it.