Coordered alignment and isoclinic stability in the rank-two complex Lu--Wenzel problem
For the complex Lu--Wenzel spectral problem, every rank-two matrix in arbitrary dimension is reduced exactly to a core of size at most four. The new core inequality lambda_1(T_X)+lambda_3(T_X)<=3 is proved on a coordered one-sided alignment layer and on the complete isoclinic layer. For each fixed epsilon>0 with the smaller singular value q>=epsilon, the isoclinic result extends to a full-direction collar of nearly equal principal angles. An explicit two-component characteristic-polynomial margin is also given on the isoclinic layer. The result does not cover the oppositely ordered alignment branch, does not give a collar uniform as q tends to zero, and gives neither an explicit nor an epsilon-independent collar threshold. It does not settle the complete rank-two layer or the full Lu--Wenzel conjecture. The rank-one formula used as a boundary calibration is prior work, and no worldwide-priority claim is made. Status: Public Beta. Internal prewriting proof, bounded-prior-art, complete-manuscript zero-trust and full-page artifact checks passed within their stated scopes. External mathematical review and formal peer review have not been completed. The archive contains the frozen manuscript, accepted TeX/PDF, five exact verification programs, the fixed zero-face guard, reproduction instructions, artifact record and checksums. The separately downloadable PDF and TeX files are identical to the accepted files inside the archive.
Authors
- Carptopus
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-18
- DOI
- https://doi.org/10.5281/zenodo.23448199
- Primary Topic
- Matrix Theory and Algorithms
- Type
- preprint