What was already known
The half-area cylinder-covering conjecture was recorded as unresolved in a 2026 survey. Earlier plank-covering results and the tetrahedral equality example did not establish a strict saving with a finite cylinder cover.
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
Disproves the half-area cylinder-covering conjecture using a regular tetrahedron.
Limitations
The selected Lean statement covers the regular tetrahedron; the manuscript’s affine extension to every nondegenerate tetrahedron is outside this selected statement.
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
- A regular tetrahedron has a finite cylinder cover with compact triangular perpendicular bases whose total area is strictly less than half its minimum orthogonal projection area.
- 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