Coordinate Subcubes of Weaver Partitions at the MSS Bound
Manuscript 14 October 2026 · Online 14 October 2026
Abstract
For a complex Parseval frame of \(m\) vectors with squared norms at most \(\alpha\), we construct an entire coordinate subcube of good signings at the historical MSS bound \(\sqrt{8\alpha}+2\alpha\). If \(0<\alpha<(3-2\sqrt{2})/2\) and \(r=\lceil(3+2\sqrt{2})/\alpha\rceil\), at least \(\lceil m/r\rceil\) signs can be chosen freely while the complement remains fixed. This gives at least \(2^{\lceil m/r\rceil}\) unordered indexed good partitions.
The proof combines an operator-small MSS partition with the sharper BCMS bound on the normalized complement. Prior counting estimates, including Akbas–Sra, are credited. This is neither a sharp count nor closure of the entire AIM agenda. The preprint is self-audited, unrefereed and AI-assisted; independent review, formal verification and absolute priority are not claimed.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete scoped theorem
- Categories
- math.FA · math.CO
- Manuscript
- 14 October 2026
- Online release
- 14 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “Coordinate Subcubes of Weaver Partitions at the MSS Bound,” EulerSolve Research Papers, AIM-ANALYSIS-0095, 2026. https://doi.org/10.5281/zenodo.23360221.
BibTeX
@misc{ferudun2026weaversubcubes,
author = {Ferudun, Alper},
title = {Coordinate Subcubes of Weaver Partitions at the MSS Bound},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/aim-analysis-0095/},
doi = {10.5281/zenodo.23360221},
note = {AIM-ANALYSIS-0095; unrefereed preprint}
}