Pith Number

pith:3M6KP63X

pith:2017:3M6KP63XZRFUDEVBJZ3Y5J7GVX

not attested not anchored not stored refs pending

Accurate Computation of the Distribution of Sums of Dependent Log-Normals with Applications to the Black-Scholes Model

Daniel MacKinlay, Robert Salomone, Zdravko Botev

arxiv:1705.03196 v2 · 2017-05-09 · stat.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3M6KP63XZRFUDEVBJZ3Y5J7GVX}

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	2026-05-18T00:42:12.032883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db3ca7fb77cc4b4192a14e778ea7e6add9a840327a2d608a221d5e15aa39c2f8

Aliases

arxiv: 1705.03196 · arxiv_version: 1705.03196v2 · doi: 10.48550/arxiv.1705.03196 · pith_short_12: 3M6KP63XZRFU · pith_short_16: 3M6KP63XZRFUDEVB · pith_short_8: 3M6KP63X

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/3M6KP63XZRFUDEVBJZ3Y5J7GVX \
  | 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: db3ca7fb77cc4b4192a14e778ea7e6add9a840327a2d608a221d5e15aa39c2f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d482ca3c754d287106a14dd4080e1abb4e6823ad6f7ead714924d2b60c56bee8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.CO",
    "submitted_at": "2017-05-09T06:22:27Z",
    "title_canon_sha256": "b03581b7227e2deefc5f6b5393d839fe74b95c79d32f7958fb567ca048784763"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.03196",
    "kind": "arxiv",
    "version": 2
  }
}