Pith Number

pith:5XUNNSO2

pith:2019:5XUNNSO2CYVMPHXAMY6NRZPD5X

not attested not anchored not stored refs pending

Minimum degree of 3-graphs without long linear paths

Jun Gao, Xinmin Hou, Yue Ma

arxiv:1903.04162 v1 · 2019-03-11 · 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{5XUNNSO2CYVMPHXAMY6NRZPD5X}

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.

Receipt and verification

First computed	2026-05-17T23:51:36.322963Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ede8d6c9da162ac79ee0663cd8e5e3eddf81e8b8e657012611ad555ecd2a1474

Aliases

arxiv: 1903.04162 · arxiv_version: 1903.04162v1 · doi: 10.48550/arxiv.1903.04162 · pith_short_12: 5XUNNSO2CYVM · pith_short_16: 5XUNNSO2CYVMPHXA · pith_short_8: 5XUNNSO2

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/5XUNNSO2CYVMPHXAMY6NRZPD5X \
  | 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: ede8d6c9da162ac79ee0663cd8e5e3eddf81e8b8e657012611ad555ecd2a1474

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "505ab87c7565745d7e4bbc99cb88e9a8560140a171676059f8f7171baf09899c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-03-11T08:10:40Z",
    "title_canon_sha256": "9da0a67f2de6aae54aa6cc59db7ad7807060740f0a36411c7897ad54d97d9a00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.04162",
    "kind": "arxiv",
    "version": 1
  }
}