Pith Number

pith:J6W22DNR

pith:2026:J6W22DNRTOCOTOVBUORHG3XDRE

not attested not anchored not stored refs resolved

On the size of k-irreducible triangulations

Arnaud de Mesmay, Oscar Fontaine, Vincent Delecroix

A k-irreducible triangulation of a genus g surface has O(k² g) triangles.

arxiv:2603.20030 v2 · 2026-03-20 · cs.CG · cs.DM · math.CO

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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 prove that a k-irreducible triangulation of an orientable surface of genus g has O(k²g) triangles, which is optimal.

C2weakest assumption

The two definitions of k-irreducible are equivalent and the triangulation remains a valid triangulation after any edge contraction that would violate the girth property; this equivalence and the topological properties of orientable surfaces are invoked to derive the size bound.

C3one line summary

k-irreducible triangulations of orientable genus-g surfaces have O(k²g) triangles.

References

44 extracted · 44 resolved · 0 Pith anchors

[1] Untangling planar graphs and curves by staying positive 2022 · doi:10.1137/1.9781611977073.11

[2] D. W. Barnette and Allan L. Edelson. All 2-manifolds have finitely many minimal trian- gulations.Isr. J. Math., 67(1):123–128, 1989.doi:10.1007/BF02764905 1989 · doi:10.1007/bf02764905

[3] Generating the triangulations of the projective plane.J 1982 · doi:10.1016/0095-8956(82)90041-7

[4] On the number of labeled graphs of bounded treewidth.Eur 2018 · doi:10.1016/j.ejc.2018.02.030

[5] The geometry of Teichm¨ uller space via geodesic currents.Invent 1988 · doi:10.1007/bf01393996

Receipt and verification

First computed	2026-05-20T00:00:36.916972Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fadad0db19b84e9baa1a3a2736ee3890d9555337bef0ec8094bd403ee38bc3d

Aliases

arxiv: 2603.20030 · arxiv_version: 2603.20030v2 · doi: 10.48550/arxiv.2603.20030 · pith_short_12: J6W22DNRTOCO · pith_short_16: J6W22DNRTOCOTOVB · pith_short_8: J6W22DNR

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/J6W22DNRTOCOTOVBUORHG3XDRE \
  | 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: 4fadad0db19b84e9baa1a3a2736ee3890d9555337bef0ec8094bd403ee38bc3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4ebdab32fe01332cb29555fa3d07c3271e585d843433c0fe1c551b405378059",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2026-03-20T15:16:58Z",
    "title_canon_sha256": "0c15fad0ea2a73e8eb5a52bf5c1554fab42ebebabeef06b7c11755217d14dfdd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.20030",
    "kind": "arxiv",
    "version": 2
  }
}