Pith Number

pith:3DQNOQVN

pith:2010:3DQNOQVNTLIWVC2Q4ZMXEZ6LTB

not attested not anchored not stored refs pending

Average Degree in Graph Powers

Diego Scheide, Jessica McDonald, Matt DeVos

arxiv:1012.2950 v1 · 2010-12-14 · 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{3DQNOQVNTLIWVC2Q4ZMXEZ6LTB}

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	2026-05-18T04:33:18.980296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8e0d742ad9ad16a8b50e6597267cb987d24d5d9ce161e85a6c9ba7d78633141

Aliases

arxiv: 1012.2950 · arxiv_version: 1012.2950v1 · doi: 10.48550/arxiv.1012.2950 · pith_short_12: 3DQNOQVNTLIW · pith_short_16: 3DQNOQVNTLIWVC2Q · pith_short_8: 3DQNOQVN

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/3DQNOQVNTLIWVC2Q4ZMXEZ6LTB \
  | 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: d8e0d742ad9ad16a8b50e6597267cb987d24d5d9ce161e85a6c9ba7d78633141

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7782f2d0666bdaba1182a9910b96057de86a7e7c4509de1c8c3f334374cba991",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-14T07:43:13Z",
    "title_canon_sha256": "89caf770af94f0013d001916ec37e4ab8de20a9bd6d18305281dd611a84772a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2950",
    "kind": "arxiv",
    "version": 1
  }
}