Pith Number

pith:BSZTPNFT

pith:2012:BSZTPNFT7PWTUKSQ3O54FAMTE5

not attested not anchored not stored refs pending

Occupation times of intervals until first passage times for spectrally negative L\'evy processes

Jean-Fran\c{c}ois Renaud, Ronnie L. Loeffen, Xiaowen Zhou

arxiv:1207.1592 v1 · 2012-07-06 · 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{BSZTPNFT7PWTUKSQ3O54FAMTE5}

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	2026-05-18T03:51:36.741529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0cb337b4b3fbed3a2a50dbbbc28193277c36de9d9df3b4515253658ebbbc5437

Aliases

arxiv: 1207.1592 · arxiv_version: 1207.1592v1 · doi: 10.48550/arxiv.1207.1592 · pith_short_12: BSZTPNFT7PWT · pith_short_16: BSZTPNFT7PWTUKSQ · pith_short_8: BSZTPNFT

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/BSZTPNFT7PWTUKSQ3O54FAMTE5 \
  | 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: 0cb337b4b3fbed3a2a50dbbbc28193277c36de9d9df3b4515253658ebbbc5437

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6fcf09b09cf5965b215343e0feb4dd8729a26376091ae67445e2aea2d0f6d23",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-07-06T11:54:26Z",
    "title_canon_sha256": "406ed48a233fea4c484f642cbdbf66f414d077ca612916864eb8e89bc91a9134"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.1592",
    "kind": "arxiv",
    "version": 1
  }
}