Pith Number

pith:VRZCQAVG

pith:2011:VRZCQAVGAK6VMOZOIRMPD5P67C

not attested not anchored not stored refs pending

On some Brownian functionals and their applications to moments in lognormal and Stein stochastic volatility models

Jacek Jakubowski, Maciej Wisniewolski

arxiv:1102.0021 v1 · 2011-01-31 · 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{VRZCQAVGAK6VMOZOIRMPD5P67C}

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	2026-05-18T04:30:13.317495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac722802a602bd563b2e4458f1f5fef8bc541fe1524f41581999b3f57dd10e29

Aliases

arxiv: 1102.0021 · arxiv_version: 1102.0021v1 · doi: 10.48550/arxiv.1102.0021 · pith_short_12: VRZCQAVGAK6V · pith_short_16: VRZCQAVGAK6VMOZO · pith_short_8: VRZCQAVG

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/VRZCQAVGAK6VMOZOIRMPD5P67C \
  | 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: ac722802a602bd563b2e4458f1f5fef8bc541fe1524f41581999b3f57dd10e29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "742f16aaed0bafd8b91a3cc8cd169ae31897210f4307ce920422fde5d1c7b4f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-01-31T21:46:45Z",
    "title_canon_sha256": "ce63c74c94995765de398c8542adee28f2d217473f400fe2afb3d6a8dbde4f15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0021",
    "kind": "arxiv",
    "version": 1
  }
}