Bounds for the complex Grothendieck constant
Follow the latest progress by email.
What is the value of the complex Grothendieck constant K_G^C? Lower bounds require examples or certified criteria separating the complex bilinear and vector-valued optimization problems in Grothendieck’s inequality.
Why it matters and what counts as progress
Why it matters: Sharper bounds narrow a longstanding gap in the complex Grothendieck inequality and test new operator-norm certification methods.
What counts as progress: Improve a certified lower or upper bound, or develop a sharp criterion that narrows the gap between them.
How the problem developed
- 1987 · Upper bound [1]
Uffe Haagerup Improved the upper bound for the complex Grothendieck constant to approximately 1.40491.
- 7 Sept 2026 · Lower bound [2]
Guo, Fang, and Lu; bound discovered by Odin Automatic AI Research Agent Proved that the complex Grothendieck constant exceeds 1.35584631827168, with computer-assisted interval verification.
AI contribution
An Improved Lower Bound for the Complex Grothendieck Constant
Guo, Fang and Lu prove the strict bound K_G^C>1.35584631827168 using a Gaussian Hermite multiplier, exact rational parameters and a weighted operator-norm criterion.
Sources
Website timeline
Publication dates and editorial changes.
AI-discovered lower bound for the complex Grothendieck constant