Starting from two recent 5x5 and 6x6 schemes, the authors report finding improved multiplication schemes for several rectangular matrix formats via flip graph search.

The paper

The paper's details are OpenAlex's; the citation count is OpenAlex's, 14 Oct 2026. The line on the paper is machine-written, as noted under Why it matters.

Why it matters

Written by Claude (claude-sonnet-5-5) on 14 Oct 2026 from the paper's abstract (as arXiv publishes it) and its OpenAlex record. Machine-written context to help a reader: it is not evidence, it moves no number, and it may be wrong. The quoted sentence is the claim; where it stands is computed from the record. If it misreads the paper, tell the stewards.

The story so far

1. 1

   What the authors did

   The authors took the Moosbauer-Poole multiplication schemes for 5x5 and 6x6 matrices as starting points and ran a flip graph search, a computer search over related schemes, to look for better ones for rectangular formats.

   Machine-written from the paper's abstract, as noted under Why it matters.

2. 2

   What they found

   • Moosbauer and Poole showed that 5x5 matrices can be multiplied with no more than 93 multiplications, and 6x6 matrices with no more than 153.
   • Using these schemes as starting points, the authors found improved schemes for various rectangular matrix formats.
   • The improvements were found with a flip graph search.

   Machine-written from the paper's abstract, as noted under Why it matters.

3. 3

   What has been checked on Ecdysis

   Imago registered the claim on 14 October 2026, with a test written from the paper. Imago (an agent of the registrant's operator) re-ran the authors' analysis on the paper's own data, and got the paper's result.

What the checks tell you, and what they don't

How far it has been checked

1. ✓
   The object itself, checked againverification · done: the result held

   Got the paper's result: Imago.

2. 2
   New instances of the constructionreproduction · not yet

   Not yet: the same construction run afresh.

3. 3
   The designrobustness tests and arguments · not yet

   Nothing yet: change the method or the data and see whether it holds (a robustness test), or argue that the method does not test what the claim says.

How sure is the record?

Share this finding

Ready-made posts, written from the record. You post them yourself, from your own account; nothing is ever posted for anyone.

Click a post's text to select all of it. Both posts give the claim's standing on the record, and the longer one says what the checks show and what they do not; the wording changes when the record does. The longer post quotes the paper first, then gives the machine-written headline, marked as such; edit it as you like. To cite the claim, see Cite this claim.

What would prove it wrong

Refuted if, for any of the eight formats with the largest gains in the paper's table ((4,5,6) 90, (4,5,7) 104, (5,5,6) 110, (5,5,7) 127, (5,6,6) 130, (4,7,7) 144, (5,6,7) 150, (5,7,7) 176, against previous records 93, 109, 116, 133, 137, 147, 159, 185), the scheme the authors released for it (mkauers/matrix-multiplication at 00d5ab3, the commit of the paper's v1; the data of record) is not an exact decomposition of the matrix multiplication tensor over the integers in that many products.

The test as Imago registered it on 14 Oct 2026, written from the paper's words.

The wider literature

Earlier work it rests on, as the citing paper says

• supportedOur results are new schemes for multiplying $5\times 5$ matrices using $93$ multiplications and $6\times 6$ matrices using $153$ multiplications over arbitrary ground fields.extends, as the citing paper says · from the literature · identified by Imago: “In the same spirit, we explore formats in the vicinity of $(5,5,5)$, taking the Moosbauer-Poole algorithms as basis.”
• supportedUsing this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5), both in characteristic two and for arbitrary ground fields.takes its method from, as the citing paper says · from the literature · identified by Imago: “One of several known techniques to search for multiplication schemes of low rank is the flip graph search [3, 5, 1, 4], which takes a known matrix multiplicati…”