Pith Number

pith:7P3HMEKJ

pith:2016:7P3HMEKJYADG5ZNBQXIB4IR3AS

not attested not anchored not stored refs pending

Densities of 3-vertex graphs

Andrzej Grzesik, Daniel Kral, Jan Volec, Ping Hu, Roman Glebov, Tamas Hubai

arxiv:1610.02446 v3 · 2016-10-07 · 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{7P3HMEKJYADG5ZNBQXIB4IR3AS}

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	2026-05-18T00:46:39.523010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbf6761149c0066ee5a185d01e223b04bb0b3b76d7166a430cdb95c98da22e01

Aliases

arxiv: 1610.02446 · arxiv_version: 1610.02446v3 · doi: 10.48550/arxiv.1610.02446 · pith_short_12: 7P3HMEKJYADG · pith_short_16: 7P3HMEKJYADG5ZNB · pith_short_8: 7P3HMEKJ

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/7P3HMEKJYADG5ZNBQXIB4IR3AS \
  | 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: fbf6761149c0066ee5a185d01e223b04bb0b3b76d7166a430cdb95c98da22e01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcbeeb12071f6b38093e557939661b357fad72cd346105e5d653298e4e1b3ca9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-10-07T23:43:14Z",
    "title_canon_sha256": "36eb430f3d0cd3115fbaa1832e2c221f7b9d1caa135e896217f2fc1c77a47799"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.02446",
    "kind": "arxiv",
    "version": 3
  }
}