Pith Number

pith:UWX3SOYP

pith:2011:UWX3SOYPU75XHPZFE2TAOJERJF

not attested not anchored not stored refs pending

Spectral properties of a class of random walks on locally finite groups

Alexander Bendikov, Barbara Bobikau, Christophe Pittet

arxiv:1102.1952 v1 · 2011-02-09 · math.SP · math.GR · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UWX3SOYPU75XHPZFE2TAOJERJF}

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	2026-05-18T01:07:57.202644Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5afb93b0fa7fb73bf2526a60724914950d9ee5bf757eadb80c3480af4d68297

Aliases

arxiv: 1102.1952 · arxiv_version: 1102.1952v1 · doi: 10.48550/arxiv.1102.1952 · pith_short_12: UWX3SOYPU75X · pith_short_16: UWX3SOYPU75XHPZF · pith_short_8: UWX3SOYP

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/UWX3SOYPU75XHPZFE2TAOJERJF \
  | 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: a5afb93b0fa7fb73bf2526a60724914950d9ee5bf757eadb80c3480af4d68297

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "472612a2d4724be829e94b13a8565fdf204846087bfa5fdc99a34e29550728b5",
    "cross_cats_sorted": [
      "math.GR",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-02-09T19:42:17Z",
    "title_canon_sha256": "73ed82a73b0f24ebcd87a4b1ec8e7df9545c66374bab457d4b5ee49e7e8eb93e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1952",
    "kind": "arxiv",
    "version": 1
  }
}