Pith Number

pith:NEVJSTM4

pith:2017:NEVJSTM4AKHAYDJCQFJQH3TCLH

not attested not anchored not stored refs pending

Periodic $p$-adic Gibbs measures of $q$-states Potts model on Cayley tree: The chaos implies the vastness of $p$-adic Gibbs measures

Lingmin Liao (LAMA), Mansoor Saburov, Mohd Ali Khameini Ahmad (LAMA)

arxiv:1708.02152 v1 · 2017-08-07 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NEVJSTM4AKHAYDJCQFJQH3TCLH}

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	2026-05-18T00:38:31.922615Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

692a994d9c028e0c0d22815303ee6259ea4d5cf747aeaab6ef50864410c2236b

Aliases

arxiv: 1708.02152 · arxiv_version: 1708.02152v1 · doi: 10.48550/arxiv.1708.02152 · pith_short_12: NEVJSTM4AKHA · pith_short_16: NEVJSTM4AKHAYDJC · pith_short_8: NEVJSTM4

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/NEVJSTM4AKHAYDJCQFJQH3TCLH \
  | 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: 692a994d9c028e0c0d22815303ee6259ea4d5cf747aeaab6ef50864410c2236b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2212e790a615838112b86c1fd13fda954b663b93a83a822a077dbc22f5edd453",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-08-07T15:06:31Z",
    "title_canon_sha256": "7ae576355dfff8186b05ecd2d7e3c4f82f19aafddd18e6373dca5dc7ecd780f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.02152",
    "kind": "arxiv",
    "version": 1
  }
}