Pith Number

pith:WNYQFY7O

pith:2013:WNYQFY7OKB25CLFO2VEXRHCW6W

not attested not anchored not stored refs pending

Last-Hitting Times and Williams' Decomposition of the Bessel Process of Dimension 3 at its Ultimate Minimum

F. Thomas Bruss, Marc Yor

arxiv:1301.2527 v1 · 2013-01-11 · 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{WNYQFY7OKB25CLFO2VEXRHCW6W}

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	2026-05-18T03:36:37.657987Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b37102e3ee5075d12caed549789c56f591c817828e9a7be791e3760bb8cc337e

Aliases

arxiv: 1301.2527 · arxiv_version: 1301.2527v1 · doi: 10.48550/arxiv.1301.2527 · pith_short_12: WNYQFY7OKB25 · pith_short_16: WNYQFY7OKB25CLFO · pith_short_8: WNYQFY7O

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/WNYQFY7OKB25CLFO2VEXRHCW6W \
  | 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: b37102e3ee5075d12caed549789c56f591c817828e9a7be791e3760bb8cc337e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b72847c4e0982321c6f58205744c709882e9406397cad4ff7512eb93e39fc5c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-01-11T15:58:36Z",
    "title_canon_sha256": "3cf6978c2d22481a0247902a9e7af4a218dfc8ff9118b3306e4e293e53d86d30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.2527",
    "kind": "arxiv",
    "version": 1
  }
}