Pith Number

pith:25SHVMX4

pith:2014:25SHVMX4XJY4UVM4O7SM6BS3RG

not attested not anchored not stored refs pending

Dynamics for the mean-field random-cluster model

Alistair Sinclair, Antonio Blanca

arxiv:1412.6180 v2 · 2014-12-18 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{25SHVMX4XJY4UVM4O7SM6BS3RG}

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	2026-05-18T01:37:01.922153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7647ab2fcba71ca559c77e4cf065b89a2afde8e56cd31b9ad3c7a94891e7b4f

Aliases

arxiv: 1412.6180 · arxiv_version: 1412.6180v2 · doi: 10.48550/arxiv.1412.6180 · pith_short_12: 25SHVMX4XJY4 · pith_short_16: 25SHVMX4XJY4UVM4 · pith_short_8: 25SHVMX4

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/25SHVMX4XJY4UVM4O7SM6BS3RG \
  | 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: d7647ab2fcba71ca559c77e4cf065b89a2afde8e56cd31b9ad3c7a94891e7b4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df57a459ae57b574374df05281aed010f5e1825623d3048f73bbfe14d10f90eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-12-18T23:34:03Z",
    "title_canon_sha256": "c64926359816481ce2449bfc6dcd6e5e99fb6421793e9cb51a4ea13404efcd47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.6180",
    "kind": "arxiv",
    "version": 2
  }
}