Pith Number

pith:NEEVB7QE

pith:2014:NEEVB7QEC26LWQJRVRC5F5KSWW

not attested not anchored not stored refs pending

A (forgotten) upper bound for the spectral radius of a graph

Chia-an Liu, Clive Elphick

arxiv:1409.2538 v2 · 2014-09-08 · 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{NEEVB7QEC26LWQJRVRC5F5KSWW}

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	2026-05-18T02:41:03.245157Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

690950fe0416bcbb4131ac45d2f552b584dbcba62080ba28195fdfca42999d6f

Aliases

arxiv: 1409.2538 · arxiv_version: 1409.2538v2 · doi: 10.48550/arxiv.1409.2538 · pith_short_12: NEEVB7QEC26L · pith_short_16: NEEVB7QEC26LWQJR · pith_short_8: NEEVB7QE

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/NEEVB7QEC26LWQJRVRC5F5KSWW \
  | 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: 690950fe0416bcbb4131ac45d2f552b584dbcba62080ba28195fdfca42999d6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a5ba317c880f2b7337bc12f28058c5693f683d66c7898664ad915138a13f00f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-09-08T22:09:24Z",
    "title_canon_sha256": "7d82fabf4e8703e84253a8314323ce9a6ae12d78744cae89a0b98c0d753ad2a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.2538",
    "kind": "arxiv",
    "version": 2
  }
}