Pith Number

pith:ASFYABEE

pith:2016:ASFYABEEWK2PNXPY5J7NHJFU3T

not attested not anchored not stored refs pending

Phase transitions for Quantum Markov Chains associated with Ising type models on a Cayley tree

Abdessatar Barhoumi, Abdessatar Souissi, Farrukh Mukhamedov

arxiv:1605.04546 v1 · 2016-05-15 · math-ph · cond-mat.stat-mech · math.FA · math.MP · math.OA · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ASFYABEEWK2PNXPY5J7NHJFU3T}

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	2026-05-18T01:14:46.871461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

048b800484b2b4f6ddf8ea7ed3a4b4dcf5d3b67af77b5027d691e3038a93b6be

Aliases

arxiv: 1605.04546 · arxiv_version: 1605.04546v1 · doi: 10.48550/arxiv.1605.04546 · pith_short_12: ASFYABEEWK2P · pith_short_16: ASFYABEEWK2PNXPY · pith_short_8: ASFYABEE

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/ASFYABEEWK2PNXPY5J7NHJFU3T \
  | 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: 048b800484b2b4f6ddf8ea7ed3a4b4dcf5d3b67af77b5027d691e3038a93b6be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7390d29a063845af3c8bdf333437e8073f6ba9b7b7c96198de601c16725b1c04",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.FA",
      "math.MP",
      "math.OA",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-05-15T13:30:07Z",
    "title_canon_sha256": "67f3150705902e5cc704ebbe8a3201b14c02070ae52529f585cd4ef56548c1c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.04546",
    "kind": "arxiv",
    "version": 1
  }
}