Pith Number

pith:IBWD2YST

pith:2011:IBWD2YST2IKJUPPA754N35WJH6

not attested not anchored not stored refs pending

Fat Hoffman graphs with smallest eigenvalue at least $-1-\tau$

Akihiro Munemasa, Tetsuji Taniguchi, Yoshio Sano

arxiv:1111.7284 v4 · 2011-11-30 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IBWD2YST2IKJUPPA754N35WJH6}

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	2026-05-18T02:21:28.192276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

406c3d6253d2149a3de0ff78ddf6c93f9ce04ddae2c679afa060c59b345566ec

Aliases

arxiv: 1111.7284 · arxiv_version: 1111.7284v4 · doi: 10.48550/arxiv.1111.7284 · pith_short_12: IBWD2YST2IKJ · pith_short_16: IBWD2YST2IKJUPPA · pith_short_8: IBWD2YST

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/IBWD2YST2IKJUPPA754N35WJH6 \
  | 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: 406c3d6253d2149a3de0ff78ddf6c93f9ce04ddae2c679afa060c59b345566ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9db2ca79c1d4bb2e239a7039605a67d04337f96fda850790da1b0fcfa8b06d8",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-11-30T19:35:31Z",
    "title_canon_sha256": "a2001ee1002f7987b8d1e977d4d2fd42b1f887bad945015cd34e86875bba9f9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.7284",
    "kind": "arxiv",
    "version": 4
  }
}