Pith Number

pith:Z3YXYKE3

pith:2013:Z3YXYKE3GEBO3RYDYFLR6MBBMI

not attested not anchored not stored refs pending

Some explicit formulas for the Brownian bridge, Brownian meander and Bessel process under uniform sampling

IUF), Marc Yor (LPMA, Mathieu Rosenbaum (LPMA)

arxiv:1311.1900 v1 · 2013-11-08 · 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{Z3YXYKE3GEBO3RYDYFLR6MBBMI}

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	2026-05-18T03:07:42.701427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cef17c289b3102edc703c1571f30216211dcbcff03b6c4d663526dd541bb146d

Aliases

arxiv: 1311.1900 · arxiv_version: 1311.1900v1 · doi: 10.48550/arxiv.1311.1900 · pith_short_12: Z3YXYKE3GEBO · pith_short_16: Z3YXYKE3GEBO3RYD · pith_short_8: Z3YXYKE3

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/Z3YXYKE3GEBO3RYDYFLR6MBBMI \
  | 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: cef17c289b3102edc703c1571f30216211dcbcff03b6c4d663526dd541bb146d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1a30622f9b7f42dec0b7de12e02e880a8ff00768effe098640e558ba59d479f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-11-08T08:35:17Z",
    "title_canon_sha256": "37384a1db3955f75346b5505506a59f508713d7740ecdf05200dab47db7ede63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1900",
    "kind": "arxiv",
    "version": 1
  }
}