Pith Number

pith:APWOO6MH

pith:2010:APWOO6MH7OWMLV76GHKKI5SOIU

not attested not anchored not stored refs pending

On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes

Marc Yor, Paavo Salminen

arxiv:1012.2038 v1 · 2010-12-09 · 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{APWOO6MH7OWMLV76GHKKI5SOIU}

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	2026-05-18T04:33:49.131843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03ece77987fbacc5d7fe31d4a4764e451943f93671062762ad35e179db8cd495

Aliases

arxiv: 1012.2038 · arxiv_version: 1012.2038v1 · doi: 10.48550/arxiv.1012.2038 · pith_short_12: APWOO6MH7OWM · pith_short_16: APWOO6MH7OWMLV76 · pith_short_8: APWOO6MH

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/APWOO6MH7OWMLV76GHKKI5SOIU \
  | 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: 03ece77987fbacc5d7fe31d4a4764e451943f93671062762ad35e179db8cd495

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1503811a98f2ffa1a3f2a114192fd37cb1662848916176b33238d5c00ca0338",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-09T15:52:37Z",
    "title_canon_sha256": "4bb1f07aab2e819c58c2fd3d72d716a9bf14102d7ce082db9bcdb587c4bc0b88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2038",
    "kind": "arxiv",
    "version": 1
  }
}