Pith Number

pith:56KML5TU

pith:2013:56KML5TUD2BKK476HALDKJD34T

not attested not anchored not stored refs pending

On the Longest Paths and the Diameter in Random Apollonian Networks

Abbas Mehrabian, Cristiane M. Sato, Ehsan Ebrahimzadeh, Jonathan Zung, Linda Farczadi, Nick Wormald, Pu Gao

arxiv:1303.5213 v1 · 2013-03-21 · 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{56KML5TUD2BKK476HALDKJD34T}

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	2026-05-18T03:30:13.601589Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef94c5f6741e82a573fe381635247be4e9d3e1972b3d6f02ee7980864103db54

Aliases

arxiv: 1303.5213 · arxiv_version: 1303.5213v1 · doi: 10.48550/arxiv.1303.5213 · pith_short_12: 56KML5TUD2BK · pith_short_16: 56KML5TUD2BKK476 · pith_short_8: 56KML5TU

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/56KML5TUD2BKK476HALDKJD34T \
  | 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: ef94c5f6741e82a573fe381635247be4e9d3e1972b3d6f02ee7980864103db54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "900eea0ea02f620e6830039ba4d86f0633d3d21362eae3214b8b6eaf34f90857",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-03-21T09:52:09Z",
    "title_canon_sha256": "cce32dfc70974ef27944f0e00967deed3deb64580bee084b058e14826e10127c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.5213",
    "kind": "arxiv",
    "version": 1
  }
}