Pith Number

pith:NCVK3TBE

pith:2006:NCVK3TBEE6BC633IRIS4PH5DOH

not attested not anchored not stored refs pending

Vertex labeling and routing in expanded Apollonian networks

Andr\'e Raspaud, Francesc Comellas, Guillaume Fertin, Lili Rong, Shuigeng Zhou, Zhongzhi Zhang

arxiv:physics/0610281 v1 · 2006-10-31 · physics.soc-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NCVK3TBEE6BC633IRIS4PH5DOH}

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	2026-05-18T04:08:52.593560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68aaadcc2427822f6f688a25c79fa371d4a51a1ec36cd9e4170c638144f9332e

Aliases

arxiv: physics/0610281 · arxiv_version: physics/0610281v1 · doi: 10.48550/arxiv.physics/0610281 · pith_short_12: NCVK3TBEE6BC · pith_short_16: NCVK3TBEE6BC633I · pith_short_8: NCVK3TBE

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/NCVK3TBEE6BC633IRIS4PH5DOH \
  | 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: 68aaadcc2427822f6f688a25c79fa371d4a51a1ec36cd9e4170c638144f9332e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06b51f1715430a1739ab7ea92bfb3b48c03aedcd7985ec2df5530a607a2290b8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2006-10-31T09:20:16Z",
    "title_canon_sha256": "724b620c59606af7f0798da1b7756c24fe7df4ae3371cfd7d8d17af4d34f3119"
  },
  "schema_version": "1.0",
  "source": {
    "id": "physics/0610281",
    "kind": "arxiv",
    "version": 1
  }
}