Pith Number

pith:VCO57Y7K

pith:2018:VCO57Y7KV4QBC6YYYQSAPAHR37

not attested not anchored not stored refs pending

Existence of phase transition for percolation using the Gaussian Free Field

Aran Raoufi, Ariel Yadin, Franco Severo, Hugo Duminil-Copin, Subhajit Goswami

arxiv:1806.07733 v2 · 2018-06-20 · math.PR · math-ph · math.GR · 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{VCO57Y7KV4QBC6YYYQSAPAHR37}

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	2026-07-05T02:01:08.609658Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a89ddfe3eaaf20117b18c4240780f1dff22f2b9552d9acce9351de37713eaee6

Aliases

arxiv: 1806.07733 · arxiv_version: 1806.07733v2 · doi: 10.48550/arxiv.1806.07733 · pith_short_12: VCO57Y7KV4QB · pith_short_16: VCO57Y7KV4QBC6YY · pith_short_8: VCO57Y7K

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/VCO57Y7KV4QBC6YYYQSAPAHR37 \
  | 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: a89ddfe3eaaf20117b18c4240780f1dff22f2b9552d9acce9351de37713eaee6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0574b66a04425f4667bd0a8b86f4971c87399c16c85331c60ad2e8dcf19e94cf",
    "cross_cats_sorted": [
      "math-ph",
      "math.GR",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-06-20T13:53:44Z",
    "title_canon_sha256": "88cde482419178bd8a93b57180b1b245b95ceaae474289b225d5fb0de574fa54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.07733",
    "kind": "arxiv",
    "version": 2
  }
}