Research Article · Preprint Mathematics
Strong permanent contraction on four-row bipartite supports through six columns
- Primary subject
- Mathematics
- Subject subfields
- Linear Algebra and Matrix Inequalities
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 2 · Permanent link
Overview
Abstract
We prove that every complex positive semidefinite matrix A supported in K_(4,6) satisfies per(|A|^2)≤per(A)∏_i a_(ii). The normalized off-diagonal block is a four-by-six operator contraction. For squared entries at most 7/10, the proof combines a four-vertex overlap estimate with a fixed mixture of rectangular permanent bounds. Separate affinity, deletion of inactive rows and piecewise separate concavity reduce the remaining inequality to fifteen rational corner values. A convex-border argument covers larger entries for every number of columns, using Lieb's block inequality and the published three-row theorem. Arbitrary phases, missing edges and singular endpoints are included. The four-by-four and four-by-five conclusions follow by padding.
Keywords permanent inequalities · positive semidefinite matrices · bipartite supports · matrix contractions · scalar certificates · Chollet conjecture
Scope of the work
Analytic strong permanent contraction through six columns on four-row complex bipartite supports, together with an arbitrary-column large-entry transfer based on the cited three-row theorem.
Reproduction notes
The paper has 8 pages. The editable-source archive contains 9 files. Compile manuscript/main.tex. The three standard-library verifier scripts check the scalar budget, pair identity and border expansion.
The manuscript
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The complete manuscript, as published in this edition.
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Author disclosures
AI-assisted preparation and internal verification are disclosed in the paper. Internal checks are distinct from external human refereeing or formal proof-assistant verification. Classical ingredients and the published three-row predecessor are attributed; the paper states the limits of the available prior-work comparison.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). Strong permanent contraction on four-row bipartite supports through six columns (Version 2). Luminary Research Archive. https://research.luminaryoddities.com/strong-permanent-contraction-four-row-bipartite-supports-through-six-columns/v/2
BibTeX
@techreport{luminary_strong_permanent_contraction_four_row_bipartite_supports_through_six_columns_v2,
title = {Strong permanent contraction on four-row bipartite supports through six columns},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 2},
url = {https://research.luminaryoddities.com/strong-permanent-contraction-four-row-bipartite-supports-through-six-columns/v/2}
}Loading discussion…