What was already known
Known graph and two-dimensional examples did not cover d≥3. Earlier higher-dimensional constructions bounded top-face incidence at codimension-one faces, which is weaker than bounding vertex degree.
AI involvement
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
Supplies the missing higher-dimensional bounded-vertex-degree coboundary expanders.
Limitations
The new formalized construction covers d≥3; graph and two-dimensional cases are separate prior results, and constants may depend on d.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every integer d≥3, there are arbitrarily large finite pure connected d-dimensional simplicial complexes with uniformly bounded vertex degree and uniform F₂ coboundary expansion in every degree below d.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
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
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision