Pith Number

pith:4K5TCTSR

pith:2019:4K5TCTSREPGBIFNZKVQ3JXNKJB

not attested not anchored not stored refs pending

On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field

Leonid V. Bogachev, Utkir A. Rozikov

arxiv:1903.11440 v2 · 2019-03-27 · math-ph · math.MP · 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{4K5TCTSREPGBIFNZKVQ3JXNKJB}

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	2026-05-17T23:39:24.545278Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2bb314e5123cc1415b95561b4ddaa485be549a9446e43d8fccc9cd126261197

Aliases

arxiv: 1903.11440 · arxiv_version: 1903.11440v2 · doi: 10.48550/arxiv.1903.11440 · pith_short_12: 4K5TCTSREPGB · pith_short_16: 4K5TCTSREPGBIFNZ · pith_short_8: 4K5TCTSR

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/4K5TCTSREPGBIFNZKVQ3JXNKJB \
  | 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: e2bb314e5123cc1415b95561b4ddaa485be549a9446e43d8fccc9cd126261197

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b05278ebace8cc7f2bf0d0b3c25487e4b17e7b8ebba63aea7ce0dfb57a2c739",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2019-03-27T14:17:48Z",
    "title_canon_sha256": "55565e890bc9c4710240d30a4748c4fbb6c99305e2eea478820400ea6b23e8e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.11440",
    "kind": "arxiv",
    "version": 2
  }
}