Pith Number

pith:ELFNZF5U

pith:2011:ELFNZF5UWD7U7NB56JUC5MLKQS

not attested not anchored not stored refs pending

Random interlacements and the Gaussian free field

Alain-Sol Sznitman

arxiv:1102.2077 v2 · 2011-02-10 · 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{ELFNZF5UWD7U7NB56JUC5MLKQS}

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	2026-05-18T03:42:12.037415Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22cadc97b4b0ff4fb43df2682eb16a84864a02383672c4aca13a11f126f47dc1

Aliases

arxiv: 1102.2077 · arxiv_version: 1102.2077v2 · doi: 10.48550/arxiv.1102.2077 · pith_short_12: ELFNZF5UWD7U · pith_short_16: ELFNZF5UWD7U7NB5 · pith_short_8: ELFNZF5U

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/ELFNZF5UWD7U7NB56JUC5MLKQS \
  | 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: 22cadc97b4b0ff4fb43df2682eb16a84864a02383672c4aca13a11f126f47dc1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6cc57c36f20f40b3ea96bba236979e4ee2dfeb9213a30f6bf652de2ca282115",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-02-10T10:52:23Z",
    "title_canon_sha256": "10ff439f6a3bba18e97d376a350fbedbc227d700662924908e70448d2a5d635b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.2077",
    "kind": "arxiv",
    "version": 2
  }
}