Pith Number

pith:Y5QFG2WK

pith:2010:Y5QFG2WKCQKCRRK334PWPPYUXI

not attested not anchored not stored refs pending

The component sizes of a critical random graph with given degree sequence

Adrien Joseph

arxiv:1012.2352 v3 · 2010-12-10 · 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{Y5QFG2WKCQKCRRK334PWPPYUXI}

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	2026-05-18T02:43:02.788773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c760536aca141428c55bdf1f67bf14ba0982c78cdb32586d5216903345b33e2f

Aliases

arxiv: 1012.2352 · arxiv_version: 1012.2352v3 · doi: 10.48550/arxiv.1012.2352 · pith_short_12: Y5QFG2WKCQKC · pith_short_16: Y5QFG2WKCQKCRRK3 · pith_short_8: Y5QFG2WK

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/Y5QFG2WKCQKCRRK334PWPPYUXI \
  | 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: c760536aca141428c55bdf1f67bf14ba0982c78cdb32586d5216903345b33e2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1c91b3e3b7d2d00345f3102f22775c67d1677bb5c3c5c3cdfa46f6e7454f0ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-10T19:11:00Z",
    "title_canon_sha256": "67b948112264a21b4358e8cfd039ef170043af63ad807c4366a262a06cff4dfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2352",
    "kind": "arxiv",
    "version": 3
  }
}