Pith Number

pith:FENJDL7X

pith:2013:FENJDL7XNHT4FKO6K5VJMRGCYB

not attested not anchored not stored refs pending

A lower bound of the least signless Laplacian eigenvalue of a graph

Guanglong Yu, Shu-Guang Guo, Yong-Gao Chen

arxiv:1311.3096 v1 · 2013-11-13 · 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{FENJDL7XNHT4FKO6K5VJMRGCYB}

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	2026-05-18T03:07:13.110810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

291a91aff769e7c2a9de576a9644c2c04a2cda073fc855511a1cf498ba861154

Aliases

arxiv: 1311.3096 · arxiv_version: 1311.3096v1 · doi: 10.48550/arxiv.1311.3096 · pith_short_12: FENJDL7XNHT4 · pith_short_16: FENJDL7XNHT4FKO6 · pith_short_8: FENJDL7X

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/FENJDL7XNHT4FKO6K5VJMRGCYB \
  | 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: 291a91aff769e7c2a9de576a9644c2c04a2cda073fc855511a1cf498ba861154

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81646527728e78a2a33c5b426d22194e2b86ac2e06bbd6ee2e61e4bd9ce77ad1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-11-13T12:03:02Z",
    "title_canon_sha256": "238f7f74c467e6e8acc7454a3c537974e9538e8ccbf315ad2a4463356f1650a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.3096",
    "kind": "arxiv",
    "version": 1
  }
}