Pith Number

pith:2IPXRQMW

pith:2018:2IPXRQMWU5L4XIEY6GO7LIOWWO

not attested not anchored not stored refs pending

On coupling and vacant set level set percolation

Alain-Sol Sznitman

arxiv:1807.10719 v1 · 2018-07-27 · 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{2IPXRQMWU5L4XIEY6GO7LIOWWO}

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	2026-05-17T23:48:33.983002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d21f78c196a757cba098f19df5a1d6b3a4b6556e1ac82a60e54fa8649bac67f2

Aliases

arxiv: 1807.10719 · arxiv_version: 1807.10719v1 · doi: 10.48550/arxiv.1807.10719 · pith_short_12: 2IPXRQMWU5L4 · pith_short_16: 2IPXRQMWU5L4XIEY · pith_short_8: 2IPXRQMW

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/2IPXRQMWU5L4XIEY6GO7LIOWWO \
  | 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: d21f78c196a757cba098f19df5a1d6b3a4b6556e1ac82a60e54fa8649bac67f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0327be1724ea4147e94f9393e026a607b68745d3708e43304a45e5b8e6a2154c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-07-27T16:45:11Z",
    "title_canon_sha256": "fea266eb897b937b06d28cff284b406a1522ceb456fe7524d9d50e815e834d95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.10719",
    "kind": "arxiv",
    "version": 1
  }
}