Pith Number

pith:S5ZCGRU2

pith:2010:S5ZCGRU2GZCYFS4XCBC56YC37U

not attested not anchored not stored refs pending

Phase separation in random cluster models III: circuit regularity

Alan Hammond

arxiv:1001.1529 v4 · 2010-01-10 · 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{S5ZCGRU2GZCYFS4XCBC56YC37U}

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	2026-05-18T02:10:03.325468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

977223469a364582cb971045df605bfd36e756f5ec811ac380b28c682b89c5fb

Aliases

arxiv: 1001.1529 · arxiv_version: 1001.1529v4 · doi: 10.48550/arxiv.1001.1529 · pith_short_12: S5ZCGRU2GZCY · pith_short_16: S5ZCGRU2GZCYFS4X · pith_short_8: S5ZCGRU2

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/S5ZCGRU2GZCYFS4XCBC56YC37U \
  | 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: 977223469a364582cb971045df605bfd36e756f5ec811ac380b28c682b89c5fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8ac6224b7e7bce8bc6cca361d69815767e72a577f3fd62568715eebf699d119",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-01-10T16:26:52Z",
    "title_canon_sha256": "95c10c6f5dbdc50b8bfe08dc2dd0672f3b190aadfffae812bfdb448c14d699e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.1529",
    "kind": "arxiv",
    "version": 4
  }
}