Pith Number

pith:VHPBKNXK

pith:2013:VHPBKNXKESJBNF4FKZDBZCDCBK

not attested not anchored not stored refs pending

A family of density expansions for L\'evy-type processes

Andrea Pascucci, Matthew Lorig, Stefano Pagliarani

arxiv:1312.7328 v1 · 2013-12-27 · math.PR · q-fin.CP · q-fin.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{VHPBKNXKESJBNF4FKZDBZCDCBK}

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	2026-05-18T03:03:45.085353Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9de1536ea249216978556461c88620ab6a38bc8e8102f09e279aeccc7a8b454

Aliases

arxiv: 1312.7328 · arxiv_version: 1312.7328v1 · doi: 10.48550/arxiv.1312.7328 · pith_short_12: VHPBKNXKESJB · pith_short_16: VHPBKNXKESJBNF4F · pith_short_8: VHPBKNXK

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/VHPBKNXKESJBNF4FKZDBZCDCBK \
  | 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: a9de1536ea249216978556461c88620ab6a38bc8e8102f09e279aeccc7a8b454

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ad71033ded09e12b85af5045d9887424f4544e48644de2faeacb6449dcf2538",
    "cross_cats_sorted": [
      "q-fin.CP",
      "q-fin.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-27T20:09:12Z",
    "title_canon_sha256": "3205f68695128425a2e8c7022933337e6bbc77ff7745f99f3c9a848614f7f05e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7328",
    "kind": "arxiv",
    "version": 1
  }
}