Pith Number

pith:VTFRFZ6U

pith:2012:VTFRFZ6UY7Q5JMQ2ZX5IGHZJFW

not attested not anchored not stored refs pending

Invariant measures under random integral mappings and marginal distributions of fractional L\'evy processes

Zbigniew J. Jurek

arxiv:1206.3047 v1 · 2012-06-14 · 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{VTFRFZ6UY7Q5JMQ2ZX5IGHZJFW}

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	2026-05-18T03:42:44.205267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

accb12e7d4c7e1d4b21acdfa831f292da778d3605f387d8bd2020fec7aca4962

Aliases

arxiv: 1206.3047 · arxiv_version: 1206.3047v1 · doi: 10.48550/arxiv.1206.3047 · pith_short_12: VTFRFZ6UY7Q5 · pith_short_16: VTFRFZ6UY7Q5JMQ2 · pith_short_8: VTFRFZ6U

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/VTFRFZ6UY7Q5JMQ2ZX5IGHZJFW \
  | 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: accb12e7d4c7e1d4b21acdfa831f292da778d3605f387d8bd2020fec7aca4962

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1e41e6eefe84787613ce480687cc5bb7ca2476374658b75e9db3903b5cad426",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-14T09:23:46Z",
    "title_canon_sha256": "dd0c6b2ce7c5e26d89a12c52e443b9094254dbc4f595be26adc2fa1ad907c721"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.3047",
    "kind": "arxiv",
    "version": 1
  }
}