What was already known
Christensen's theorem gave small spatial embeddings for amenable source algebras. The unrestricted one-sided question of Cameron, Christensen, Sinclair, Smith, White and Wiggins remained open; positive two-sided results under structural hypotheses do not settle it. The construction imports Voiculescu's almost-commuting clock-and-shift obstruction.
AI involvement
The manuscript credits OpenAI as author. It draws on human near-inclusion and almost-commuting-matrix results; the individual model process and a human check of this construction are not documented.
OpenAI is the credited author of the original manuscript; the record does not establish autonomous model-level origin.
Importance
Constructs a counterexample to the unrestricted small spatial embedding question.
Limitations
Spatial embeddings still exist; the obstruction is to embeddings implemented by unitaries close to the identity under one-sided near inclusion. It does not refute two-sided Kadison–Kastler stability.
Technical verification
The TeX source provides the full construction and obstruction proof, but neither a completed human review nor a machine check of this theorem is documented.
Human understanding
The paper explains its mechanism, but no human is identified as having explained the central argument. Few is the default for missing human-understanding evidence.
Correction and publication history
Constructs a counterexample to the unrestricted small spatial embedding question.
Read this published revision