Pith Number

pith:2O2QXRRC

pith:2006:2O2QXRRCWM7XL23GTLHW5XYGHQ

not attested not anchored not stored refs pending

Recurrence of random walk traces

Itai Benjamini, Ori Gurel-Gurevich, Russell Lyons

arxiv:math/0603060 v3 · 2006-03-02 · 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{2O2QXRRCWM7XL23GTLHW5XYGHQ}

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	2026-07-04T15:52:43.379856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3b50bc622b33f75eb669acf6edf063c1e0fdb2208246f947e08fede2a0980cc

Aliases

arxiv: math/0603060 · arxiv_version: math/0603060v3 · doi: 10.48550/arxiv.math/0603060 · pith_short_12: 2O2QXRRCWM7X · pith_short_16: 2O2QXRRCWM7XL23G · pith_short_8: 2O2QXRRC

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/2O2QXRRCWM7XL23GTLHW5XYGHQ \
  | 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: d3b50bc622b33f75eb669acf6edf063c1e0fdb2208246f947e08fede2a0980cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "276fde8bbc525d092e98032f7c52fc535c751670122a73b5941ae44254017712",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2006-03-02T21:18:33Z",
    "title_canon_sha256": "33c552a1312e4a9b8473021a941f15721aafebacff8bcdc5bf3a2320a08a5713"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0603060",
    "kind": "arxiv",
    "version": 3
  }
}