Pith Number

pith:FQOERV3Y

pith:2011:FQOERV3YQOBATMSCU6ODYRBF5A

not attested not anchored not stored refs pending

A series of trees with the first $\lfloor\frac{n-7}{2}\rfloor$ largest energies

Chang-Xiang He, Hai-Ying Shan, Jia-Yu Shao, Li Zhang

arxiv:1111.2084 v1 · 2011-11-09 · 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{FQOERV3YQOBATMSCU6ODYRBF5A}

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	2026-05-18T04:08:44.189152Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c1c48d778838209b242a79c3c4425e831323159486d3abb0cdeba026f892d90

Aliases

arxiv: 1111.2084 · arxiv_version: 1111.2084v1 · doi: 10.48550/arxiv.1111.2084 · pith_short_12: FQOERV3YQOBA · pith_short_16: FQOERV3YQOBATMSC · pith_short_8: FQOERV3Y

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/FQOERV3YQOBATMSCU6ODYRBF5A \
  | 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: 2c1c48d778838209b242a79c3c4425e831323159486d3abb0cdeba026f892d90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c41db8bdd7c0ca17b4651f5c22571ab69113e909c9e32fceb2d48e2b911c8f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-11-09T00:21:26Z",
    "title_canon_sha256": "9bc6050d96f4c0a9fc1103bf4448ae9228b28f0c49900782c7fdbb7c42a38a74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2084",
    "kind": "arxiv",
    "version": 1
  }
}