Pith Number

pith:PU3Q7HQF

pith:2011:PU3Q7HQF3YDUNDFKTGKDIMP7X6

not attested not anchored not stored refs pending

The Wiener Index of Unicyclic Graphs with Girth and the Matching Number

Xiao-Dong Zhang, Ya-Hong Chen

arxiv:1102.5409 v1 · 2011-02-26 · 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{PU3Q7HQF3YDUNDFKTGKDIMP7X6}

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	2026-05-18T04:27:47.004984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d370f9e05de07468caa99943431ffbfadbdcc82096dd28725afda24a51404a2

Aliases

arxiv: 1102.5409 · arxiv_version: 1102.5409v1 · doi: 10.48550/arxiv.1102.5409 · pith_short_12: PU3Q7HQF3YDU · pith_short_16: PU3Q7HQF3YDUNDFK · pith_short_8: PU3Q7HQF

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/PU3Q7HQF3YDUNDFKTGKDIMP7X6 \
  | 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: 7d370f9e05de07468caa99943431ffbfadbdcc82096dd28725afda24a51404a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7756654002ee7f8ce38a9089917e74dc44c40b0daaa47ffd184b437e6de8bf0e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-26T13:26:33Z",
    "title_canon_sha256": "dd6d1872223d18af8488efcc8d15733177e440c3a808b2d9b3b3530f12c9673f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.5409",
    "kind": "arxiv",
    "version": 1
  }
}