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

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
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Coordered alignment and isoclinic stability in the rank-two complex Lu--Wenzel problem

Carptopus
Zenodo (CERN European Organization for Nuclear Research)
Matrix Theory and Algorithms
preprint

Coordered alignment and isoclinic stability in the rank-two complex Lu--Wenzel problem

Carptopus
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Matrix Theory and Algorithms
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.