What was already known
Dey’s O(n^(4/3)) bound was the classical general upper bound for halving lines; earlier work progressed from an O(n^(3/2)) scale.
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
Gives a fixed power improvement over the longstanding planar halving-line bound.
Limitations
The constants are existential and ineffective in the manuscript; n must be even and the point set in general position.
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
- Some absolute ε>0 and C bound the number of unordered halving pairs in every sufficiently large even n-point planar set with no three collinear by Cn^(4/3−ε).
- 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