Pith Number

pith:PAMN7CEN

pith:2026:PAMN7CEN4L77QHYLKYDXKY7EJA

not attested not anchored not stored refs resolved

Branch-width of represented matroids in matrix multiplication time

Mujin Choi, Sang-il Oum, Tuukka Korhonen

A matroid given by an n by n matrix over a finite field has a branch-decomposition of width at most k found in O(n²) time plus one matrix multiplication, or the algorithm reports that branch-width exceeds k.

arxiv:2605.14428 v1 · 2026-05-14 · cs.DS · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PAMN7CEN4L77QHYLKYDXKY7EJA}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

For an n-element matroid M given by an n × n matrix representation over a finite field F and an integer k, we present an (O_{k,F}(n²)+O(n^ω))-time algorithm that either finds a branch-decomposition of M of width at most k, or confirms that the branch-width of M is more than k.

C2weakest assumption

The input matroid is supplied as a matrix representation over a finite field F; the algorithm's hidden factors that depend on k and F are computable, and the overhead of converting to standard form is accounted for when the matrix is not already in that form.

C3one line summary

O(n² + n^ω)-time algorithm decides if branch-width of a matrix-represented matroid over a finite field is at most k.

References

24 extracted · 24 resolved · 0 Pith anchors

[1] Josh Alman, Ran Duan, Virginia Vassilevska Williams, Yinzhan Xu, Zixuan Xu, and Renfei Zhou, More asymmetry yields faster matrix multiplication , Proceedings of the 2025 Annual ACM-SIAM Symposium on D 2025

[2] Hans L. Bodlaender and Ton Kloks, Efficient and constructive algorithms for the pathwidth and treewidth of graphs, J. Algorithms 21 (1996), no. 2, 358–402. MR 98g:68122 27 1996

[3] Bunch and John E 1974

[4] Bruno Courcelle, The monadic second-order logic of graphs I: Recognizable sets of ﬁnite graphs , Inform. and Comput. 85 (1990), no. 1, 12–75. MR 91g:05107 1990

[5] 138, Cambridge University Press, Cam- bridge, 2012 2012

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:07.167883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7818df888de2fff81f0b56077563e44803a03f94f442e280d4371793bd0acb38

Aliases

arxiv: 2605.14428 · arxiv_version: 2605.14428v1 · doi: 10.48550/arxiv.2605.14428 · pith_short_12: PAMN7CEN4L77 · pith_short_16: PAMN7CEN4L77QHYL · pith_short_8: PAMN7CEN

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PAMN7CEN4L77QHYLKYDXKY7EJA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7818df888de2fff81f0b56077563e44803a03f94f442e280d4371793bd0acb38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7f4e11a10bba13fc6b6bb3f43f7fd9c6fa38975a53f388d654bdfed7f7af182",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-14T06:19:53Z",
    "title_canon_sha256": "743d7b221a935709ce8f8cfb67302c1eda5b538bf470f57d87828c0003839287"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14428",
    "kind": "arxiv",
    "version": 1
  }
}