Pith Number

pith:AIQG2CIJ

pith:2025:AIQG2CIJEKXMO2WKVDJJ2QMIIZ

not attested not anchored not stored refs pending

Largest $3$-uniform set systems with VC-dimension $2$

Jian Wang, Shengtong Zhang, Zixiang Xu

arxiv:2505.07756 v1 · 2025-05-12 · 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{AIQG2CIJEKXMO2WKVDJJ2QMIIZ}

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.

Cited by

2 papers in Pith

A disproof of the uniform witness conjecture

Beating the Ahlswede--Khachatrian bound for the Erd\H{o}s--Frankl--Pach problem

Receipt and verification

First computed	2026-07-05T11:01:52.839683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02206d090922aec76acaa8d29d418846553e8f4b4cf3f525f899db132cd33075

Aliases

arxiv: 2505.07756 · arxiv_version: 2505.07756v1 · doi: 10.48550/arxiv.2505.07756 · pith_short_12: AIQG2CIJEKXM · pith_short_16: AIQG2CIJEKXMO2WK · pith_short_8: AIQG2CIJ

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/AIQG2CIJEKXMO2WKVDJJ2QMIIZ \
  | 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: 02206d090922aec76acaa8d29d418846553e8f4b4cf3f525f899db132cd33075

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4903a4967197ac567237cd06a3902230d92fa72f1c881bf778392493218a72ec",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-05-12T17:02:25Z",
    "title_canon_sha256": "123b0e5d9cc6f42db84ce8ced4352d10094227c60a97a0d8b17541db4468e07a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.07756",
    "kind": "arxiv",
    "version": 1
  }
}