Pith Number

pith:WOV44ZNG

pith:2012:WOV44ZNGCDUTS7JOSX2VPP2QFA

not attested not anchored not stored refs pending

On the probability of planarity of a random graph near the critical point

Juanjo Ru\'e, Marc Noy, Vlady Ravelomanana

arxiv:1204.3376 v2 · 2012-04-16 · 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{WOV44ZNGCDUTS7JOSX2VPP2QFA}

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	2026-05-18T03:56:44.697529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3abce65a610e9397d2e95f557bf5028368a9fbac39a0bb318d36a6ce0a0c478

Aliases

arxiv: 1204.3376 · arxiv_version: 1204.3376v2 · doi: 10.48550/arxiv.1204.3376 · pith_short_12: WOV44ZNGCDUT · pith_short_16: WOV44ZNGCDUTS7JO · pith_short_8: WOV44ZNG

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/WOV44ZNGCDUTS7JOSX2VPP2QFA \
  | 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: b3abce65a610e9397d2e95f557bf5028368a9fbac39a0bb318d36a6ce0a0c478

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de3a42c0a08f0bccecfc928296d96a51a6794a85b9eb701f52d3204a728878e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-04-16T07:14:14Z",
    "title_canon_sha256": "07da1c1a1a9f2eb9b65c071832e3b729d12c56547c18823043a2077b036fb31f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3376",
    "kind": "arxiv",
    "version": 2
  }
}