Pith Number

pith:CQKLUYM6

pith:2012:CQKLUYM6KWOW7SJUS2B63UMMIN

not attested not anchored not stored refs pending

The asymptotic number of different rooted trees of a tree

Xueliang Li, Yiyang Li, Yongtang Shi

arxiv:1207.3915 v2 · 2012-07-17 · 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{CQKLUYM6KWOW7SJUS2B63UMMIN}

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	2026-05-18T03:25:25.719044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1414ba619e559d6fc9349683edd18c4356d86275296b7528e2d88b76eb68336c

Aliases

arxiv: 1207.3915 · arxiv_version: 1207.3915v2 · doi: 10.48550/arxiv.1207.3915 · pith_short_12: CQKLUYM6KWOW · pith_short_16: CQKLUYM6KWOW7SJU · pith_short_8: CQKLUYM6

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/CQKLUYM6KWOW7SJUS2B63UMMIN \
  | 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: 1414ba619e559d6fc9349683edd18c4356d86275296b7528e2d88b76eb68336c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "101c41e78a0581d599b787cf13dc031e73ba855ec80d4da11ba1c34d61984362",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-17T08:44:04Z",
    "title_canon_sha256": "85030019b3893ee41ec751f0249775a52338a5b1625dc158222e649157f02c3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3915",
    "kind": "arxiv",
    "version": 2
  }
}