For every number of variables n and every normalized bounded ratio R on Lorentzian polynomials in n variables, the optimal bounding constant of R is at most 2: operatornameopt(R)≤ 2.

Huang–Huh–Soskin–Wang conjecture on bounded ratios of Lorentzian polynomials

The conjecture predicts that every normalized bounded ratio of Lorentzian objects has optimal bounding constant at most $2$ . The 2025 authors established this in dimensions $n \le 5$ and reported computational support through $n \le 6$ , but left the general statement open.

Known results

Huang, Huh, Soskin, and Wang (2025): bounded ratios are characterized through the dual of the cut cone.
Huang, Huh, Soskin, and Wang (2025): the pentagonal inequality has optimal constant $4$ when all five indices are distinct.
Huang, Huh, Soskin, and Wang (2025): the conjectured bound $2$ follows for $n \le 5$ ; computations support it for $n \le 6$ .

September 2026 counterexample

A new preprint claims an explicit bounded ratio arising from a non-hypermetric clique-web facet, contradicting the conjectured description. It also proposes a general rational-polyhedral tropical cone characterization. This is an unrefereed and presently unverified refutation.

Current status (as of September 2026): The conjecture is claimed false by an unrefereed preprint, while its proposed counterexample and replacement characterization remain unverified.

Huang–Huh–Soskin–Wang conjecture on bounded ratios of Lorentzian polynomials

Primary source

Additional references

Progress summary

Solutions 0