Hatami's conjecture (2021): every Boolean matrix of bounded Schur-multiplier norm is a signed sum of boundedly many blocky matrices; equivalently, every idempotent Schur multiplier is a finite signed sum of contractive idempotent Schur multipliers (the matrix analogue of the Green-Sanders quantitative Cohen idempotent theorem).
Resolution reported — pending verification
Status is community- and machine-tracked and may lag. Verify independently before investing effort.
Assessment
Renown 2/5
A named conjecture with a dedicated literature, known to the operator-space and communication-complexity communities.
Attackability 1/5
A uniform-boundedness claim over all dimensions; no finite counterexample witness. Proof territory, and proof is how it fell.
- finite witness
- 1/5
- oracle cost
- 1/5
- freshness
- 2/5
- seedability
- 1/5
Reported resolution
proof by Hamed Hatami and student coauthors on .
Announced by Hatami as his most-wanted problem since 2021, solved with four student coauthors; paper 'A characterization of idempotent Schur multipliers' on arXiv (identifier to be attached by curator; announced today, not yet indexed). Prior best bound (polylogarithmic in dimension) was Goh-Hatami arXiv:2506.21752.
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
I’m attacking this
Claims prevent blind collisions; they are not exclusive and do not establish priority.