Pith Number

pith:52VNVKCT

pith:2012:52VNVKCTVNJS36AB3B4HVNSYZO

not attested not anchored not stored refs pending

Trees with given degree sequences that have minimal subtrees

Xiao-Dong Zhang, Xiu-Mei Zhang

arxiv:1209.0273 v1 · 2012-09-03 · 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{52VNVKCTVNJS36AB3B4HVNSYZO}

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	2026-05-18T03:46:29.541725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eeaadaa853ab532df801d8787ab658cbb81e2b4a52755b074578269d912e53fb

Aliases

arxiv: 1209.0273 · arxiv_version: 1209.0273v1 · doi: 10.48550/arxiv.1209.0273 · pith_short_12: 52VNVKCTVNJS · pith_short_16: 52VNVKCTVNJS36AB · pith_short_8: 52VNVKCT

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/52VNVKCTVNJS36AB3B4HVNSYZO \
  | 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: eeaadaa853ab532df801d8787ab658cbb81e2b4a52755b074578269d912e53fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85dff320a9daf2e4b16d426cf0f6289621db1afaf0b7731e7da6eadf0b192235",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-03T08:49:07Z",
    "title_canon_sha256": "2b98e4a18502f1bc95de36940a358a3920c57e9fa0df9ca326531353238a783a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0273",
    "kind": "arxiv",
    "version": 1
  }
}