OpenAI · 125-02 · 2026-09-24 · Theoretical computer science
The approximation threshold for metric k-median
preprints/The-Approximation-Threshold-for-Metric-k-Median-September-24-2026
Family 125. The approximation threshold for metric -median.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Gives a deterministic polynomial-time -approximation for finite rational metric -median with specified candidate facilities, for every fixed . Assuming , the optimal infimum approximation factor is .
For every fixed ε > 0, we give a deterministic polynomial-time -approximation for finite rational metric k-median with specified candidate facilities, opening at most k facilities. Under , the infimum approximation factor in this model is therefore .
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
This preprint is named in the Lean scope note for 125: The metric <i>k</i>-median approximation threshold and recovery. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.