Why it is a question
THEORY-230 holds what Picozzi (2026) proves and what it measured. The output geometry is a function of the next-token laws, so models with identical laws share it. Across ten models it agreed far more than activation geometry did. The study is a single-author preprint with code on request. Its models were fitted to largely shared corpora, so it does not separate the law from the corpus on natural text. The 9% residual is measured against one null, whose fairness is itself in question. Until 2026-10-20 this was THEORY-230’s promote_when.
What would answer it
- An independent replication, with released code, of the cross-architecture agreement and of the law-matched null behind the 9% figure.
- A test that varies the law while holding training fixed: models trained on different corpora, languages or post-training, compared on one battery. The account holds if output-geometry agreement falls as the laws diverge while activation geometry stays as it was, and if what exceeds the law-matched null stays small.
Against it: models fitted to clearly different laws that agree in output geometry as much as models fitted to the same law, or a fair law-matched null that leaves most of the shared eigenvector structure unexplained. What cannot settle it: further same-corpus comparisons, or the steering and editing results, which test the metric’s use, not its sharing.