Pith Number

pith:T7EROFZR

pith:2010:T7EROFZRA7AM3X3GY2KJEKTXGO

not attested not anchored not stored refs pending

On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two

Farrukh Mukhamedov, Luigi Accardi, Mansoor Saburov

arxiv:1004.3623 v2 · 2010-04-21 · math-ph · math.DS · math.FA · 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{T7EROFZRA7AM3X3GY2KJEKTXGO}

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	2026-05-18T04:04:06.990074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fc917173107c0cddf66c694922a7733aa5ab974e4018562ed0bb4427a935d7b

Aliases

arxiv: 1004.3623 · arxiv_version: 1004.3623v2 · doi: 10.48550/arxiv.1004.3623 · pith_short_12: T7EROFZRA7AM · pith_short_16: T7EROFZRA7AM3X3G · pith_short_8: T7EROFZR

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/T7EROFZRA7AM3X3GY2KJEKTXGO \
  | 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: 9fc917173107c0cddf66c694922a7733aa5ab974e4018562ed0bb4427a935d7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60735bdcf6ca97b0216e0914753f4e0e99140a0a8023199cbbc7879cf23c0921",
    "cross_cats_sorted": [
      "math.DS",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-04-21T05:40:20Z",
    "title_canon_sha256": "d845e0e30d1dd59a2982b6e55b3d3b91fbf42b68c9c91aca23a803778f9752b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.3623",
    "kind": "arxiv",
    "version": 2
  }
}