Pith Number

pith:WWWYOQMZ

pith:2009:WWWYOQMZWH6OOT3OA326ZF7GWF

not attested not anchored not stored refs pending

Toughness and Vertex Degrees

D. Bauer, E. Schmeichel, H.J. Broersma, J. van den Heuvel, N. Kahl

arxiv:0912.2919 v2 · 2009-12-15 · 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{WWWYOQMZWH6OOT3OA326ZF7GWF}

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	2026-05-18T04:21:13.738005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5ad874199b1fce74f6e06f5ec97e6b1589076b7ff9e3bcd39e8eb75d93fc4c1

Aliases

arxiv: 0912.2919 · arxiv_version: 0912.2919v2 · doi: 10.48550/arxiv.0912.2919 · pith_short_12: WWWYOQMZWH6O · pith_short_16: WWWYOQMZWH6OOT3O · pith_short_8: WWWYOQMZ

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/WWWYOQMZWH6OOT3OA326ZF7GWF \
  | 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: b5ad874199b1fce74f6e06f5ec97e6b1589076b7ff9e3bcd39e8eb75d93fc4c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29017ebf545b6bb5cc02719702cc2ddf2fe014a31754b2b67caeb0491f45622c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-12-15T15:10:31Z",
    "title_canon_sha256": "bd9a54b5e86ee4cbe1f25bc8f36fefe1f468ec1dc3b42fd3e56c385665b2bacb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.2919",
    "kind": "arxiv",
    "version": 2
  }
}