Pith Number

pith:VVZPGAJF

pith:2008:VVZPGAJFDNU4RLKMSYA6LZXCXX

not attested not anchored not stored refs pending

Fluctuation theory and exit systems for positive self-similar Markov processes

Andreas Kyprianou, Juan Carlos Pardo, Lo\"ic Chaumont, V\'ictor Rivero

arxiv:0812.2506 v2 · 2008-12-13 · 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{VVZPGAJFDNU4RLKMSYA6LZXCXX}

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	2026-05-18T03:39:03.854536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad72f301251b69c8ad4c9601e5e6e2bde941fca5304e5efc3ed6d81972aaff38

Aliases

arxiv: 0812.2506 · arxiv_version: 0812.2506v2 · doi: 10.48550/arxiv.0812.2506 · pith_short_12: VVZPGAJFDNU4 · pith_short_16: VVZPGAJFDNU4RLKM · pith_short_8: VVZPGAJF

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/VVZPGAJFDNU4RLKMSYA6LZXCXX \
  | 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: ad72f301251b69c8ad4c9601e5e6e2bde941fca5304e5efc3ed6d81972aaff38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e95d95c88a4c73bd1998b02a25e0a40f04a9365e44ca1d460a469f332c7ae297",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-12-13T00:27:18Z",
    "title_canon_sha256": "e57e2fe9376d05b9c0c9571312eb44b60f1159d872aee6caa4f2eea0020a31e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.2506",
    "kind": "arxiv",
    "version": 2
  }
}