Pith Number

pith:JHZQEUH3

pith:2011:JHZQEUH3MSYLB3UOXL56QXKLGS

not attested not anchored not stored refs pending

The Harary index of trees

Aleksandar Ili\' c, Guihai Yu, Lihua Feng

arxiv:1104.0920 v3 · 2011-04-05 · 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{JHZQEUH3MSYLB3UOXL56QXKLGS}

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	2026-05-18T04:21:29.724744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49f30250fb64b0b0ee8ebafbe85d4b34b38a13867b7ca6fb10ba445b414954ce

Aliases

arxiv: 1104.0920 · arxiv_version: 1104.0920v3 · doi: 10.48550/arxiv.1104.0920 · pith_short_12: JHZQEUH3MSYL · pith_short_16: JHZQEUH3MSYLB3UO · pith_short_8: JHZQEUH3

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/JHZQEUH3MSYLB3UOXL56QXKLGS \
  | 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: 49f30250fb64b0b0ee8ebafbe85d4b34b38a13867b7ca6fb10ba445b414954ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43dbaaab2d5eaf6f96adc232be5bf021beb657c09fe7390fa15eab81c05000dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-04-05T19:43:04Z",
    "title_canon_sha256": "1fb1519acf1702d60c41845aac64c0482cd5739f85bcb72c463de03132642360"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.0920",
    "kind": "arxiv",
    "version": 3
  }
}