Pith Number

pith:X3KUDVRQ

pith:2010:X3KUDVRQKS6ZXMDDDRLUDZ2HCA

not attested not anchored not stored refs pending

On the range, local times and periodicity of random walk on an interval

Balint Toth, Siva Athreya, Sunder Sethuraman

arxiv:1009.3999 v1 · 2010-09-21 · 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{X3KUDVRQKS6ZXMDDDRLUDZ2HCA}

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	2026-05-18T04:40:34.737796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bed541d63054bd9bb0631c5741e747101996290d24ab33ec070f69de27ce4186

Aliases

arxiv: 1009.3999 · arxiv_version: 1009.3999v1 · doi: 10.48550/arxiv.1009.3999 · pith_short_12: X3KUDVRQKS6Z · pith_short_16: X3KUDVRQKS6ZXMDD · pith_short_8: X3KUDVRQ

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/X3KUDVRQKS6ZXMDDDRLUDZ2HCA \
  | 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: bed541d63054bd9bb0631c5741e747101996290d24ab33ec070f69de27ce4186

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1312ca1c8f2296b56f348380b5600b7ec8e26cc694d78992f198ed65bd13851a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-09-21T05:46:41Z",
    "title_canon_sha256": "e31965157c26c35cb2f0edced8db2146bf251a250a417c725ee55cfecdacd589"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3999",
    "kind": "arxiv",
    "version": 1
  }
}