Polynomial-factor hardness of Euclidean closest vector

The problem asks whether Euclidean closest vector is NP-hard to approximate within a fixed polynomial factor under deterministic reductions.

Known results

• Dinur, Kindler, and Safra: ordinary closest vector is hard to approximate within $n^{c/\log\log n}$ for some $c>0$, which is weaker than a fixed polynomial factor.
• For $p\notin 2\mathbb{Z}$, constant-factor hardness results are known under Gap-SETH; the Euclidean case $p=2$ is excluded.

Undated polynomial-factor hardness claim

A source titled “NP-Hardness of Approximating the Closest Vector Problem within a Polynomial Factor” states that $\mathrm{GapCVP}_{n}^{c'}$ is NP-hard under deterministic polynomial-time Karp reductions, apparently implying the requested result. No independently corroborating preprint or peer-reviewed artifact was found.

Current status (as of March 2026): A direct source claims the result for $\mathrm{GapCVP}_{n}^{c'}$, but corroboration is absent; without it, the claim is unverified.