Pith Number

pith:JO7DYUX3

pith:2013:JO7DYUX3KBNMWT3U4IMOMKKP5H

not attested not anchored not stored refs pending

On Quantum Markov Chains on Cayley tree III: Ising model

Farrukh Mukhamedov, Luigi Accardi, Mansoor Saburov

arxiv:1311.6545 v2 · 2013-11-26 · math-ph · math.DS · math.MP · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JO7DYUX3KBNMWT3U4IMOMKKP5H}

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	2026-05-18T01:23:26.675154Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bbe3c52fb505acb4f74e218e6294fe9f32ffa37d9fd6249b1484130ea0443bd

Aliases

arxiv: 1311.6545 · arxiv_version: 1311.6545v2 · doi: 10.48550/arxiv.1311.6545 · pith_short_12: JO7DYUX3KBNM · pith_short_16: JO7DYUX3KBNMWT3U · pith_short_8: JO7DYUX3

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/JO7DYUX3KBNMWT3U4IMOMKKP5H \
  | 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: 4bbe3c52fb505acb4f74e218e6294fe9f32ffa37d9fd6249b1484130ea0443bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ed068a1238166df9b1cb9b6e7739facc514c3bc9dab52f5761418f7ff5b6602",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-11-26T03:07:01Z",
    "title_canon_sha256": "46e7ad2cd535092e31334b633b6d31beaa78783c9858b368413eb39c28ba57eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.6545",
    "kind": "arxiv",
    "version": 2
  }
}