Pith Number

pith:UB7XL3Z4

pith:2010:UB7XL3Z4F64RJ66HNEKDGQFA5Z

not attested not anchored not stored refs pending

Phase separation in random cluster models I: uniform upper bounds on local deviation

Alan Hammond

arxiv:1001.1527 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{UB7XL3Z4F64RJ66HNEKDGQFA5Z}

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	2026-05-18T04:20:13.260423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a07f75ef3c2fb914fbc769143340a0ee6450773665fea1f8cc1f2d379aeedaf7

Aliases

arxiv: 1001.1527 · arxiv_version: 1001.1527v4 · doi: 10.48550/arxiv.1001.1527 · pith_short_12: UB7XL3Z4F64R · pith_short_16: UB7XL3Z4F64RJ66H · pith_short_8: UB7XL3Z4

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/UB7XL3Z4F64RJ66HNEKDGQFA5Z \
  | 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: a07f75ef3c2fb914fbc769143340a0ee6450773665fea1f8cc1f2d379aeedaf7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d05cc2299758290d4cb25ded2f745022bcce983424c5cc6244d6988762a0ec3",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-01-10T16:21:14Z",
    "title_canon_sha256": "b99da4576309116addf0cf7a0ffb36a8cea0e8c24b3c1b884ea3edc27e367d19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.1527",
    "kind": "arxiv",
    "version": 4
  }
}