Pith Number

pith:VZT3V2EM

pith:2010:VZT3V2EMTBU74BG72BPJ3ZZD24

not attested not anchored not stored refs pending

Pivotal, cluster and interface measures for critical planar percolation

Christophe Garban, G\'abor Pete, Oded Schramm

arxiv:1008.1378 v5 · 2010-08-08 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VZT3V2EMTBU74BG72BPJ3ZZD24}

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	2026-05-18T02:59:06.881813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae67bae88c9869fe04dfd05e9de723d738da3a3a74d8c58693d3a98146e8ce36

Aliases

arxiv: 1008.1378 · arxiv_version: 1008.1378v5 · doi: 10.48550/arxiv.1008.1378 · pith_short_12: VZT3V2EMTBU7 · pith_short_16: VZT3V2EMTBU74BG7 · pith_short_8: VZT3V2EM

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/VZT3V2EMTBU74BG72BPJ3ZZD24 \
  | 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: ae67bae88c9869fe04dfd05e9de723d738da3a3a74d8c58693d3a98146e8ce36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bffebd04c363b60cb223d8974d2c6f393bd2887e869f22eb95341b40fdb95994",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-08-08T03:58:42Z",
    "title_canon_sha256": "17f00fdb17424cac0f9545b324e6a18a4d84cb834fb235a785680c451640b64d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.1378",
    "kind": "arxiv",
    "version": 5
  }
}