What was already known
The higher-dimensional Duke problem asked for equidistribution of complete packets of diagonal orbits; the manuscript distinguishes a fixed local homothety packet from collections attached only to a multiplier order.
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
Establishes the prime-degree packet form of a higher-dimensional arithmetic equidistribution problem.
Limitations
The selected claim covers fixed prime degree at least five and complete volume-weighted packets. The Lean scope does not establish quartic or sextic results.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note identifies equidistribution and tightness for every fixed prime degree at least five under the stated local-type and discriminant assumptions.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For each fixed prime degree at least five, volume-weighted packets of totally real fields equidistribute to Haar measure as their multiplier-order discriminants grow, with no escape of mass, arbitrary local homothety type, and varying fields allowed.
- 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