Pith Number

pith:45JVN4YD

pith:2012:45JVN4YDYYNFZKWBRBJTLISV7W

not attested not anchored not stored refs pending

On Wiener polarity index of cactus graphs

Nan Chen, Wen-Xue Du, Yi-Zheng Fan

arxiv:1211.3513 v1 · 2012-11-15 · 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{45JVN4YDYYNFZKWBRBJTLISV7W}

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	2026-05-18T02:42:37.528181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e75356f303c61a5caac1885335a255fdb97c48f5c27e363e069871196d8d8ba3

Aliases

arxiv: 1211.3513 · arxiv_version: 1211.3513v1 · doi: 10.48550/arxiv.1211.3513 · pith_short_12: 45JVN4YDYYNF · pith_short_16: 45JVN4YDYYNFZKWB · pith_short_8: 45JVN4YD

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/45JVN4YDYYNFZKWBRBJTLISV7W \
  | 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: e75356f303c61a5caac1885335a255fdb97c48f5c27e363e069871196d8d8ba3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "439858df2cf5b0066880e836405b5371b7e99371eb2c7ab353be22b58458ef67",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-15T07:21:50Z",
    "title_canon_sha256": "a3cdb7f43ff34044f6361ec06775626bfe0128e5093f4a8fc47189d0ea4d0f59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3513",
    "kind": "arxiv",
    "version": 1
  }
}