Pith Number

pith:RWKEUL44

pith:2009:RWKEUL442KXP6MXE73DKJJXYQJ

not attested not anchored not stored refs pending

Sharp threshold for percolation on expanders

G\'abor Lugosi, Itai Benjamini, Rapha\"el Rossignol, St\'ephane Boucheron

arxiv:0906.3657 v2 · 2009-06-19 · 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{RWKEUL442KXP6MXE73DKJJXYQJ}

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	2026-05-18T03:44:58.048921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d944a2f9cd2aeff32e4fec6a4a6f8827dea604a00d3fe614d88205305a50e48

Aliases

arxiv: 0906.3657 · arxiv_version: 0906.3657v2 · doi: 10.48550/arxiv.0906.3657 · pith_short_12: RWKEUL442KXP · pith_short_16: RWKEUL442KXP6MXE · pith_short_8: RWKEUL44

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/RWKEUL442KXP6MXE73DKJJXYQJ \
  | 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: 8d944a2f9cd2aeff32e4fec6a4a6f8827dea604a00d3fe614d88205305a50e48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa6271ebfecbc2b5f301003a151ac5b60c1db023d8d08434c8b6577c4df93fb6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-06-19T12:59:51Z",
    "title_canon_sha256": "5acdb1afe5d3325792557482efa425f496adf7b867907cf6171942df9dbad9a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.3657",
    "kind": "arxiv",
    "version": 2
  }
}