Pith Number

pith:QLJQKHM3

pith:2012:QLJQKHM32B6K7LIXT72MDOH4LT

not attested not anchored not stored refs pending

Faber-Krahn type inequality for unicyclic graphs

Guang-Jun Zhang, Jie Zhang, Xiao-Dong Zhang

arxiv:1201.0455 v1 · 2012-01-02 · 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{QLJQKHM32B6K7LIXT72MDOH4LT}

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	2026-05-18T04:05:17.474308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82d3051d9bd07cafad179ff4c1b8fc5cc4b49f739bf1f4e39e4ddd11efac6869

Aliases

arxiv: 1201.0455 · arxiv_version: 1201.0455v1 · doi: 10.48550/arxiv.1201.0455 · pith_short_12: QLJQKHM32B6K · pith_short_16: QLJQKHM32B6K7LIX · pith_short_8: QLJQKHM3

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/QLJQKHM32B6K7LIXT72MDOH4LT \
  | 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: 82d3051d9bd07cafad179ff4c1b8fc5cc4b49f739bf1f4e39e4ddd11efac6869

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1c38181307e42beb41f362e6b540cef705a257e72a2f666527d6b01345a7a0b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-01-02T11:18:45Z",
    "title_canon_sha256": "755da3f5f70ab25aead84b9797b5b11ff092ec55a700723e35cac62c41e603b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.0455",
    "kind": "arxiv",
    "version": 1
  }
}