What was already known
Prior k-median approximation analyses exposed a bounded-price strictness effect, but the manuscript treats recovery from an imperfect supplied anchor while enforcing the exact k-facility budget.
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 polynomial-time recovery step that maintains the exact facility budget under stated anchor-quality conditions.
Limitations
This selected algorithm requires a sufficiently accurate supplied anchor, positive integral distances of polynomially bounded diameter, and only logarithmically many unrepresented comparison clusters. The separate unrestricted-metric approximation theorem has different assumptions.
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
- On positive integral metrics of polynomially bounded diameter, a supplied anchor with distinct accurate proxies for all but logarithmically many comparison clusters and sufficiently small total proxy error supports a polynomial-time k-median recovery algorithm opening at most k facilities and attaining a (1+2/e+ε) factor against those comparison centers with any requested confidence.
- 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