Pith Number

pith:B546OLTU

pith:2026:B546OLTUPARL4LXXJZXQFVQT6A

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The number $4/9$ is a non-jump for $3$-graphs

Dhruv Mubayi, Xizhi Liu

The number 4/9 is a non-jump for 3-uniform hypergraphs.

arxiv:2605.13567 v1 · 2026-05-13 · math.CO

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\pithnumber{B546OLTUPARL4LXXJZXQFVQT6A}

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2 Internet Archive

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 prove that 4/9 is a non-jump for 3-uniform hypergraphs.

C2weakest assumption

That inserting the union of a high-cogirth pair of Steiner triple systems into the B-part of the ABB pattern produces a valid construction achieving the non-jump property at 4/9.

C3one line summary

4/9 is a non-jump for 3-graphs via a perturbed ABB construction inserting high-cogirth pairs of Steiner triple systems.

References

35 extracted · 35 resolved · 0 Pith anchors

[1] R. Baber and J. Talbot. Hypergraphs do jump.Combin. Probab. Comput., 20(2):161–171, 2011 2011

[2] T. Bohman and L. Warnke. Large girth approximate Steiner triple systems.J. Lond. Math. Soc. (2), 100(3):895–913, 2019 2019

[3] W. G. Brown and M. Simonovits. Digraph extremal problems, hypergraph extremal problems, and the densities of graph structures.Discrete Math., 48(2–3):147–162, 1984 1984

[4] M. Delcourt and L. Postle. Proof of the High Girth Existence Conjecture via refined absorption,

[5] P. Erdős. On extremal problems of graphs and generalized graphs.Israel J. Math., 2:183–190, 1964. 9 1964

Cited by

1 paper in Pith

Intervals of hypergraph Tur\'an densities

Receipt and verification

First computed	2026-05-18T02:44:23.414866Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f79e72e747822be2ef74e6f02d613f021caded47a67b0871a14d1173b3edc97

Aliases

arxiv: 2605.13567 · arxiv_version: 2605.13567v1 · doi: 10.48550/arxiv.2605.13567 · pith_short_12: B546OLTUPARL · pith_short_16: B546OLTUPARL4LXX · pith_short_8: B546OLTU

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/B546OLTUPARL4LXXJZXQFVQT6A \
  | 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: 0f79e72e747822be2ef74e6f02d613f021caded47a67b0871a14d1173b3edc97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0dcbb9b48e236f356d73afadc329a67f296059a009edbea30473e2c0fbb45f3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T14:05:39Z",
    "title_canon_sha256": "1a0740d54f46dc0694ee24c77316ae1808f1beb3590a17b22598dbc03a96a6f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13567",
    "kind": "arxiv",
    "version": 1
  }
}