Pith Number

pith:PIIX72OZ

pith:2019:PIIX72OZXRG7SXU3ADUTPSJNHC

not attested not anchored not stored refs pending

Relation between the number of leaves of a tree and its diameter

Pu Qiao, Xingzhi Zhan

arxiv:1904.12150 v1 · 2019-04-27 · 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{PIIX72OZXRG7SXU3ADUTPSJNHC}

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	2026-05-17T23:47:38.843698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a117fe9d9bc4df95e9b00e937c92d38be09e968da187d29695d92ed24143dc8

Aliases

arxiv: 1904.12150 · arxiv_version: 1904.12150v1 · doi: 10.48550/arxiv.1904.12150 · pith_short_12: PIIX72OZXRG7 · pith_short_16: PIIX72OZXRG7SXU3 · pith_short_8: PIIX72OZ

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/PIIX72OZXRG7SXU3ADUTPSJNHC \
  | 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: 7a117fe9d9bc4df95e9b00e937c92d38be09e968da187d29695d92ed24143dc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7d195c1ad07835103f723b5f466eb05bcf825ab556ef1d82ba19031bdb9c4f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-04-27T11:52:14Z",
    "title_canon_sha256": "2dc0b10996124d2e15898d59362ed56eabf4215ba3e2c9af9d70b375be78e383"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.12150",
    "kind": "arxiv",
    "version": 1
  }
}