Pith Number

pith:LI53Q7LM

pith:2020:LI53Q7LMLJ4HFRDJ57SOAC67NZ

not attested not anchored not stored refs pending

Finite-size scaling, phase coexistence, and algorithms for the random cluster model on random graphs

Matthew Jenssen, Tyler Helmuth, Will Perkins

arxiv:2006.11580 v2 · 2020-06-20 · math.PR · cs.DS · 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{LI53Q7LMLJ4HFRDJ57SOAC67NZ}

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	2026-07-05T03:14:44.966735Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a3bb87d6c5a7872c469efe4e00bdf6e4b417aadeb06f05296d12f6e220bb0f1

Aliases

arxiv: 2006.11580 · arxiv_version: 2006.11580v2 · doi: 10.48550/arxiv.2006.11580 · pith_short_12: LI53Q7LMLJ4H · pith_short_16: LI53Q7LMLJ4HFRDJ · pith_short_8: LI53Q7LM

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/LI53Q7LMLJ4HFRDJ57SOAC67NZ \
  | 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: 5a3bb87d6c5a7872c469efe4e00bdf6e4b417aadeb06f05296d12f6e220bb0f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55d789f2a4dbc8a508560d4bf7d54cf805e1d2b0d4620536bf1207dc6d621c54",
    "cross_cats_sorted": [
      "cs.DS",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-06-20T14:03:48Z",
    "title_canon_sha256": "7f2884084655943dfcc140e5ef1bc446e6afc7647ae63fffc53a3da495b46700"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.11580",
    "kind": "arxiv",
    "version": 2
  }
}