Pith Number

pith:VW5JXVNE

pith:2012:VW5JXVNEJDWHOYN4FGRXGNCGBK

not attested not anchored not stored refs pending

The hitting time of zero for a stable process

Alexander R. Watson, Alexey Kuznetsov, Andreas E. Kyprianou, Juan Carlos Pardo

arxiv:1212.5153 v3 · 2012-12-20 · 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{VW5JXVNEJDWHOYN4FGRXGNCGBK}

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	2026-05-18T02:56:45.159727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adba9bd5a448ec7761bc29a37334460aa5791152547b220c178ed387850fddb2

Aliases

arxiv: 1212.5153 · arxiv_version: 1212.5153v3 · doi: 10.48550/arxiv.1212.5153 · pith_short_12: VW5JXVNEJDWH · pith_short_16: VW5JXVNEJDWHOYN4 · pith_short_8: VW5JXVNE

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/VW5JXVNEJDWHOYN4FGRXGNCGBK \
  | 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: adba9bd5a448ec7761bc29a37334460aa5791152547b220c178ed387850fddb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fa92a36edc028223773430efaffd7a610e07eafe3b5fc4a2f3f5d8135730870",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-12-20T17:29:14Z",
    "title_canon_sha256": "a75f7022ff103dd27f4db33d28872312a3669afa0f368913af066696f9c52f95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5153",
    "kind": "arxiv",
    "version": 3
  }
}