Ebenfelt’s weak SOS conjecture
The supplied sources identify Ebenfelt's weak SOS conjecture as a rank-gap assertion for sums of squares of Hermitian polynomials, but they do not state the precise hypotheses, definition of rank, or forbidden rank interval. Consequently, a complete formal statement cannot be recovered from the supplied material without adding unsupported details.
References
Primary source
Additional references
- A Proof of Ebenfelt's weak SOS Conjecture — arXiv — Zhiwei Wang, Chenlong Yue, Xiangyu Zhou
Progress summary
A new unrefereed manuscript claims to settle the conjecture and a related rigidity question, but independent confirmation is absent.
The conjecture links sums of squares of Hermitian polynomials to forbidden gaps in their ranks and to rigidity phenomena for proper maps. The September 2026 manuscript by Zhiwei Wang, Chenlong Yue, and Xiangyu Zhou claims the full rank-gap statement and derives the corresponding proper-map gap theorem.
Known results
- Huang proved the case.
- Brooks and Grundmeier proved the diagonal case for .
- Dusty and Halfpap established the real-valued diagonal case for , with partial results beyond.
- Gao and Ng (2021) found analogous rank gaps for Hermitian forms of nontrivial signature, but not the exact conjecture.
September 2026 claimed proof
The new manuscript asserts the general rank-gap theorem and a proper-map consequence, which would resolve Ebenfelt’s weak SOS conjecture. The claim is newly posted and unrefereed; the scan found no published verification, counterexample, withdrawal, or referee report.
Current status (as of September 2026): A manuscript claims a complete resolution, but that claim is unverified; restricted diagonal cases are established, while the general conjecture remains unsettled pending verification.
Solutions 0
No solutions have been posted yet.