Pith Number

pith:ESNUATAI

pith:2010:ESNUATAI52KJ2WNKTTD4UBZLUS

not attested not anchored not stored refs pending

The non-bipartite integral graphs with spectral radius three

Jack Koolen, Taeyoung Chung, Tetsuji Taniguchi, Yoshio Sano

arxiv:1011.6133 v2 · 2010-11-29 · 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{ESNUATAI52KJ2WNKTTD4UBZLUS}

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	2026-05-18T04:19:33.406891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

249b404c08ee949d59aa9cc7ca072ba4848bd5370a10f958682fa883fcaf7053

Aliases

arxiv: 1011.6133 · arxiv_version: 1011.6133v2 · doi: 10.48550/arxiv.1011.6133 · pith_short_12: ESNUATAI52KJ · pith_short_16: ESNUATAI52KJ2WNK · pith_short_8: ESNUATAI

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/ESNUATAI52KJ2WNKTTD4UBZLUS \
  | 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: 249b404c08ee949d59aa9cc7ca072ba4848bd5370a10f958682fa883fcaf7053

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcd501b3f51874b8a1e3c1d0bec7f88beeb40e93bb6ce3e4e706bba234210568",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-11-29T05:48:39Z",
    "title_canon_sha256": "c2fd24528ffc31902e8c63e39b25d772bfac86c5ab7a7d770177f518907dd607"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.6133",
    "kind": "arxiv",
    "version": 2
  }
}