What was already known
The best general candidate-facility approximation was about 2+ε, while a Max-k-Coverage reduction gave hardness approaching 1+2/e.
AI involvement
The manuscript names OpenAI as author and the release attributes these manuscripts to an internal model. The specific amount of human direction is not described.
OpenAI authorship and repository production statement attribute the claimed algorithm and proof to its internal model.
- Supporting source (github.com) — Abstract, author line
Importance
Claims to close the algorithm-versus-hardness gap for general candidate-facility metric k-median.
Limitations
The theorem gives every fixed ε>0; it does not claim an algorithm attaining exactly 1+2/e. Facility-restricted hardness is a separate question. The cited Lean documentation maps solution theorems to this claim; the comparator challenge files contain placeholders.
Technical verification
The repository reports a Lean formalization of the deterministic algorithm and the P≠NP infimum threshold. The published solution modules have claim-matching theorems main_finite_work and threshold; comparator challenge files contain intentional sorry placeholders, so the solution files and stated comparator mapping are the checking evidence.
Formal checking
Lean theorem proofs in OAI.Combinatorics.KMedian.Main.main_finite_work and Threshold.threshold mapped to published comparator challenges
- Checker
- Lean 4 kernel, as reported by OpenAI’s formalization catalogue
- Scope
- Deterministic polynomial-time (1+2/e+ε) metric k-median algorithm with at most k facilities, and conditional P≠NP infimum threshold
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation of the central directed comparison and derandomization is documented; Few is the evidence default.
Correction and publication history
Claims to close the algorithm-versus-hardness gap for general candidate-facility metric k-median.
Read this published revision