Pith Number

pith:UQULX4JV

pith:2011:UQULX4JV7WJGBU5LKHWNZXGA63

not attested not anchored not stored refs pending

On Han's Hook Length Formulas for Trees

Oliver X.Q. Gao, Peter L. Guo, William Y.C. Chen

arxiv:1103.4068 v1 · 2011-03-21 · 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{UQULX4JV7WJGBU5LKHWNZXGA63}

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	2026-05-18T04:26:21.878345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a428bbf135fd9260d3ab51ecdcdcc0f6c93614a75832b194a9d3f6e7e102d91e

Aliases

arxiv: 1103.4068 · arxiv_version: 1103.4068v1 · doi: 10.48550/arxiv.1103.4068 · pith_short_12: UQULX4JV7WJG · pith_short_16: UQULX4JV7WJGBU5L · pith_short_8: UQULX4JV

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/UQULX4JV7WJGBU5LKHWNZXGA63 \
  | 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: a428bbf135fd9260d3ab51ecdcdcc0f6c93614a75832b194a9d3f6e7e102d91e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb71c244b460d2398cbc300b969b046901a33dcdcfcd295ad1ef3781e853107b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-21T16:19:22Z",
    "title_canon_sha256": "57632c0588cb008ab9adee9c74bf17b9f26fafd861e30a7be11576becfe3f9ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4068",
    "kind": "arxiv",
    "version": 1
  }
}