Pith Number

pith:WYRWG5Q6

pith:2009:WYRWG5Q67UAZVRROQXI2QNDUTV

not attested not anchored not stored refs pending

A zero-one law for the existence of triangles in random key graphs

Armand M. Makowski, Osman Yagan

arxiv:0910.0499 v1 · 2009-10-02 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WYRWG5Q67UAZVRROQXI2QNDUTV}

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	2026-07-04T15:53:38.356921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b62363761efd019ac62e85d1a834749d5d7e0590b9ca9b0dfb50de3fff8e2c58

Aliases

arxiv: 0910.0499 · arxiv_version: 0910.0499v1 · doi: 10.48550/arxiv.0910.0499 · pith_short_12: WYRWG5Q67UAZ · pith_short_16: WYRWG5Q67UAZVRRO · pith_short_8: WYRWG5Q6

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/WYRWG5Q67UAZVRROQXI2QNDUTV \
  | 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: b62363761efd019ac62e85d1a834749d5d7e0590b9ca9b0dfb50de3fff8e2c58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5afd2c8a481e8b16ccb6cdb04304b61b8dca91a8ec69ba10e4cf19f1562318d",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-10-02T23:23:13Z",
    "title_canon_sha256": "b847d954eb81ef75182f791f5359cceadb049590224ba34ab547730d7964668d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.0499",
    "kind": "arxiv",
    "version": 1
  }
}