Pith Number

pith:PETFGJ7T

pith:2007:PETFGJ7TTNOAPGPSI3O3PTLPUZ

not attested not anchored not stored refs pending

On $p$-adic Gibbs measures of countable state Potts model on the Cayley tree

A.Yu. Khrennikov, F. M. Mukhamedov, J. F.F. Mendes

arxiv:0705.0244 v2 · 2007-05-02 · 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{PETFGJ7TTNOAPGPSI3O3PTLPUZ}

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	2026-05-18T04:37:20.962620Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79265327f39b5c0799f246ddb7cd6fa668cae88f5f805a5a9f7a684520f74c53

Aliases

arxiv: 0705.0244 · arxiv_version: 0705.0244v2 · doi: 10.48550/arxiv.0705.0244 · pith_short_12: PETFGJ7TTNOA · pith_short_16: PETFGJ7TTNOAPGPS · pith_short_8: PETFGJ7T

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/PETFGJ7TTNOAPGPSI3O3PTLPUZ \
  | 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: 79265327f39b5c0799f246ddb7cd6fa668cae88f5f805a5a9f7a684520f74c53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a3d6550ca98c58e8b9bc40d7b42ca11299435f7ab34839b670b608967170698",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2007-05-02T10:13:56Z",
    "title_canon_sha256": "870376791e959e6cde69e609465631ae80f7ce809b62a07b207a45361c3d8cb1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0705.0244",
    "kind": "arxiv",
    "version": 2
  }
}