Pith Number

pith:QV7246DF

pith:2011:QV7246DFJ3N3R6TTTJE5AGNTBI

not attested not anchored not stored refs pending

On fat Hoffman graphs with smallest eigenvalue at least -3

Akihiro Munemasa, Hye Jin Jang, Jack Koolen, Tetsuji Taniguchi

arxiv:1110.6821 v3 · 2011-10-31 · 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{QV7246DFJ3N3R6TTTJE5AGNTBI}

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	2026-05-18T03:44:24.460621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

857fae78654edbb8fa739a49d019b30a3e43f1aa991b8520e12afd3cf54d88ca

Aliases

arxiv: 1110.6821 · arxiv_version: 1110.6821v3 · doi: 10.48550/arxiv.1110.6821 · pith_short_12: QV7246DFJ3N3 · pith_short_16: QV7246DFJ3N3R6TT · pith_short_8: QV7246DF

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/QV7246DFJ3N3R6TTTJE5AGNTBI \
  | 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: 857fae78654edbb8fa739a49d019b30a3e43f1aa991b8520e12afd3cf54d88ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c175ebbf36f1eedc4d4f4a8c67febaf1eda217e204a73bc88c15376d53f860d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-10-31T15:11:31Z",
    "title_canon_sha256": "20a12bb342e2abbe28786a2637fb51c66a06f75bb29aef54ba21314c3a9b23f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6821",
    "kind": "arxiv",
    "version": 3
  }
}