Pith Number

pith:6QEYIDS3

pith:2026:6QEYIDS3J65LEDZ6P5ALSPK7KU

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A Lower Bound on the Self-intersections of Fold Singularities

Joshua Drouin, Liam Kahmeyer

A sharp lower bound exists on the number of self-intersections of fold singularities for maps from oriented surfaces to the plane.

arxiv:2605.12989 v1 · 2026-05-13 · math.GT

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Claims

C1strongest claim

We construct a sharp lower bound on the number of self-intersections of such fold singularities.

C2weakest assumption

The map is a simple stable fold map, and the connected components of the singular set can be viewed as boundary components of smaller surface components to which the immersed-boundary bound applies directly.

C3one line summary

A sharp lower bound is established on the self-intersections of fold singularities for stable maps from oriented surfaces to R^2 by reducing the problem to bounds on immersed surface boundaries.

References

17 extracted · 17 resolved · 0 Pith anchors

[1] On singularities of folding type.Mathematics of the USSR-Izvestiya, 4(5):1119–1134, Oct 1970 1970

[2] Singularities, expanders and topology of maps 2009

[3] Minimal number of self-intersections of the boundary of an immersed surface in the plane 2009

[4] Quelques remarques sur les applications diff´ erentiables d’une surface dans le plan.Annales de l’institut Fourier, 10:47–60 1960

[5] Stable maps of surfaces into the plane.Topology and its Applications, 107(3):307–316, Nov 2000 2000

Receipt and verification

First computed	2026-05-18T03:09:00.552099Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f409840e5b4fbab20f3e7f40b93d5f552a94b41be7efa982484c1929b64e8ca8

Aliases

arxiv: 2605.12989 · arxiv_version: 2605.12989v1 · doi: 10.48550/arxiv.2605.12989 · pith_short_12: 6QEYIDS3J65L · pith_short_16: 6QEYIDS3J65LEDZ6 · pith_short_8: 6QEYIDS3

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6QEYIDS3J65LEDZ6P5ALSPK7KU \
  | 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: f409840e5b4fbab20f3e7f40b93d5f552a94b41be7efa982484c1929b64e8ca8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d974788a3b150663ee41e1c682350d6139cec09799b34833e65a0bd9b32e224",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-13T04:37:54Z",
    "title_canon_sha256": "4018977c242439e9f4a0b9394ec9607f08f2f323822f49696cc8cbd33e2a0f25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12989",
    "kind": "arxiv",
    "version": 1
  }
}