What was already known
Goddyn’s thin-tree conjecture asked for arbitrarily thin trees at sufficiently high connectivity; the strong version asks for the optimal order C/k, which the manuscript says remained open.
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
Resolves the quantitative strong thin-tree conjecture at the necessary 1/k scale.
Limitations
The selected first-paper claim is existential and does not specify C or an algorithm; a separate companion formalization describes a deterministic algorithm.
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
- There is a universal C such that every finite loopless k-edge-connected multigraph on at least two vertices has a spanning tree meeting each nontrivial cut in at most C/k times the number of original cut edges.
- 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