OpenAI reports failure of maximal coarse assembly injectivity

A uniformly discrete bounded-geometry coarse disjoint union of finite connected uniformly bounded-degree graphs has an infinite-order class in degree-one coarse K-homology that maps to zero under maximal coarse assembly, so that map is not rationally injective.

Sources for this record

What was already known

The companion paper had constructed an infinite-order kernel class for ordinary reduced coarse assembly. Vanishing after passage to the reduced Roe algebra did not imply vanishing of its lift under the maximal assembly map.

AI involvement AI-led

OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.

OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.

Importance Major

Extends the graph-union counterexample to the universal maximal Roe-algebra target.

Limitations

The linked Lean note checks only the companion ordinary reduced coarse-assembly counterexample, not vanishing in the maximal Roe algebra.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.

Correction and publication history

2026-10-18 · publication

Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.

Read this published revision