Pith Number

pith:ZV5D6QES

pith:2012:ZV5D6QESOYCZWGSR6YFF5VTZH5

not attested not anchored not stored refs pending

Phase transition and level-set percolation for the Gaussian free field

Alain-Sol Sznitman, Pierre-Fran\c{c}ois Rodriguez

arxiv:1202.5172 v2 · 2012-02-23 · 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{ZV5D6QESOYCZWGSR6YFF5VTZH5}

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	2026-05-18T03:17:57.496702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd7a3f409276059b1a51f60a5ed6793f4077874bb43e533ef4f33495be7584cd

Aliases

arxiv: 1202.5172 · arxiv_version: 1202.5172v2 · doi: 10.48550/arxiv.1202.5172 · pith_short_12: ZV5D6QESOYCZ · pith_short_16: ZV5D6QESOYCZWGSR · pith_short_8: ZV5D6QES

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/ZV5D6QESOYCZWGSR6YFF5VTZH5 \
  | 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: cd7a3f409276059b1a51f60a5ed6793f4077874bb43e533ef4f33495be7584cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd9259eb50b8c6a1ca61c59b3e5e8d1ed41f19656d5747cde93af7bc99cdcef3",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-02-23T13:17:14Z",
    "title_canon_sha256": "8a32aca7b7395646cb698d42d86342a0357e467fc64ac64b79484ff7171d6b99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.5172",
    "kind": "arxiv",
    "version": 2
  }
}