Pith Number

pith:65WVFBUB

pith:2012:65WVFBUBSLTJQW3NNEBF3ZILON

not attested not anchored not stored refs pending

Symmetries of L\'evy processes on compact quantum groups, their Markov semigroups and potential theory

Anna Kula, Fabio Cipriani, Uwe Franz

arxiv:1210.6768 v2 · 2012-10-25 · math.OA · 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{65WVFBUBSLTJQW3NNEBF3ZILON}

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	2026-05-18T02:58:57.671693Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f76d52868192e6985b6d69025de50b737efc4a9020ffe25e7aebb49dd5fc8192

Aliases

arxiv: 1210.6768 · arxiv_version: 1210.6768v2 · doi: 10.48550/arxiv.1210.6768 · pith_short_12: 65WVFBUBSLTJ · pith_short_16: 65WVFBUBSLTJQW3N · pith_short_8: 65WVFBUB

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/65WVFBUBSLTJQW3NNEBF3ZILON \
  | 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: f76d52868192e6985b6d69025de50b737efc4a9020ffe25e7aebb49dd5fc8192

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07a42f98182bcfd4aa96d30fb2a9442f18ecad4ce410df93e728868f3808e140",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-10-25T09:32:17Z",
    "title_canon_sha256": "0f9f4767d7f2edc564b0b688f3c4f90dc8accb2b1bd19672ec35abf96e17a67d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6768",
    "kind": "arxiv",
    "version": 2
  }
}