What was already known
Prior first-order sampling methods had positive powers of dimension in their query bounds under fixed conditioning and accuracy; the manuscript asks whether any such power is intrinsic.
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
Determines the infimal polynomial dimension exponent of this oracle query problem to be zero.
Limitations
The model allows unrestricted measurable randomized computation between exact queries; arithmetic and bit costs are not bounded.
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 C² potentials with known minimizer at zero and I≤∇²V≤2I, exact value-and-gradient oracle sampling to total-variation error at most 1/10 uses at most Cε d^ε queries for every ε>0, while every algorithm needs at least c log d queries eventually.
- 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