Pith Number

pith:IQTM4UWY

pith:2010:IQTM4UWYAGMZS3VC7DJ3PVQYBI

not attested not anchored not stored refs pending

On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three

Farrukh Mukhamedov, Luigi Accardi, Mansoor Saburov

arxiv:1011.2256 v1 · 2010-11-10 · math-ph · math.DS · 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{IQTM4UWYAGMZS3VC7DJ3PVQYBI}

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	2026-05-18T04:04:06.900458Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4426ce52d80199996ea2f8d3b7d6180a27d8ff7437f6451488cbc5fe6cc250b4

Aliases

arxiv: 1011.2256 · arxiv_version: 1011.2256v1 · doi: 10.48550/arxiv.1011.2256 · pith_short_12: IQTM4UWYAGMZ · pith_short_16: IQTM4UWYAGMZS3VC · pith_short_8: IQTM4UWY

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/IQTM4UWYAGMZS3VC7DJ3PVQYBI \
  | 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: 4426ce52d80199996ea2f8d3b7d6180a27d8ff7437f6451488cbc5fe6cc250b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d75e9fc90df068f612e8f9a8627529639c764d4571fe1e837641ebf6f0ebf22",
    "cross_cats_sorted": [
      "math.DS",
      "math.FA",
      "math.MP",
      "math.OA",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-11-10T01:51:12Z",
    "title_canon_sha256": "b971f0a3bf0341d0ca39c42dfb7a83394fa4862c18bbf81d87978518e5e3ffb8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2256",
    "kind": "arxiv",
    "version": 1
  }
}