Pith Number

pith:M6YZHUPD

pith:2026:M6YZHUPDLZJY75CRZXCRC5JDP4

not attested not anchored not stored refs resolved

The unbreakable quasi-graphic matroids

John David Clifton, Sayantani Bhattacharya, Zach Walsh

3-connected unbreakable quasi-graphic matroids receive a complete structural characterization.

arxiv:2605.12811 v1 · 2026-05-12 · math.CO

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3 Author claim open · sign in to claim

4 Citations open

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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

We extend the latter result by giving a complete characterization of the 3-connected unbreakable quasi-graphic matroids.

C2weakest assumption

The matroid is assumed to be 3-connected and quasi-graphic; the characterization relies on the prior structural theory of quasi-graphic matroids developed in the cited literature.

C3one line summary

A complete characterization of the 3-connected unbreakable quasi-graphic matroids is provided, with the lifted-graphic case obtained as a corollary.

References

15 extracted · 15 resolved · 0 Pith anchors

[1] N. Bowler, D. Funk, and D. Slilaty. Describing quasi-graphic matroids.European J. Combin., 85:103062, 26, 2020 2020

[2] Describing quasi-graphic matroids 2020

[3] R. Chen and J. Geelen. Infinitely many excluded minors for frame matroids and for lifted-graphic matroids.J. Combin. Theory Ser. B, 133:46–53, 2018 2018

[4] R. Chen and G. Whittle. On recognizing frame and lifted-graphic matroids.J. Graph Theory, 87(1):72–76, 2018 2018

[5] C. Cho, J. Oxley, and S. Wang. The symmetric strong circuit elimination property. Adv. in Appl. Math., 173(part A):Paper No. 102983, 2026 2026

Receipt and verification

First computed	2026-05-18T03:09:12.457536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67b193d1e35e538ff451cdc51175237f3618b5dfd1d53d7827c15594a7515bc2

Aliases

arxiv: 2605.12811 · arxiv_version: 2605.12811v1 · doi: 10.48550/arxiv.2605.12811 · pith_short_12: M6YZHUPDLZJY · pith_short_16: M6YZHUPDLZJY75CR · pith_short_8: M6YZHUPD

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/M6YZHUPDLZJY75CRZXCRC5JDP4 \
  | 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: 67b193d1e35e538ff451cdc51175237f3618b5dfd1d53d7827c15594a7515bc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd9776afadfb48a3093e012f437177a058fc8c07cd6f2650fc92d696306e3919",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-12T23:11:48Z",
    "title_canon_sha256": "50c4627a55560581be6c191795d1f318ddab3580204d30577fdc762b39d3764c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12811",
    "kind": "arxiv",
    "version": 1
  }
}