What was already known
Earlier work established orders and upper bounds for the leftover edges. Joos and Kühn conjectured the sharp asymptotic constant; this paper addresses its triangle specialization.
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
Proves the sharp terminal-leave constant for the triangle-removal process.
Limitations
The result is the triangle case of a broader hypergraph conjecture; it does not prove the sharp constant for other removed subgraphs.
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 random triangle removal from Kₙ, the number of edges left at termination divided by n^(3/2) converges in L² to 1/(2√2).
- 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