The work function algorithm is k-competitive on every metric space

The preprint claims the strong form of the deterministic $k$-server conjecture: for every metric space and initial configuration $C_0$, $\mathrm{WFA}_{C_0}(\sigma) \le k\,\mathrm{OPT}_{C_0}(\sigma) + \mathrm{cl}(C_0)$. The work function is represented as a matrix whose $k$-column determinants (in a min-plus-to-formal-algebra dictionary) are work-function values, and the amortised analysis uses a potential on a larger matrix indexed by pairs of entries. The authors proved $k=3$ themselves and credit the model with the general-$k$ algebraic proof, which they adapted. It would close the 30-year gap between $k$ and the $2k-1$ bound of Koutsoupias–Papadimitriou.