Pith Number

pith:TJOJHKZJ

pith:2005:TJOJHKZJBDYFZPMOYNKBS4HCZ6

not attested not anchored not stored refs pending

Almost Sure Recurrence of the Simple Random Walk Path

Itai Benjamini, Ori Gurel-Gurevich

arxiv:math/0508270 v2 · 2005-08-15 · math.PR · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TJOJHKZJBDYFZPMOYNKBS4HCZ6}

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	2026-07-04T15:13:21.415688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a5c93ab2908f05cbd8ec3541970e2cfaee14919a9a146ea1a3dd86567f696ae

Aliases

arxiv: math/0508270 · arxiv_version: math/0508270v2 · doi: 10.48550/arxiv.math/0508270 · pith_short_12: TJOJHKZJBDYF · pith_short_16: TJOJHKZJBDYFZPMO · pith_short_8: TJOJHKZJ

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/TJOJHKZJBDYFZPMOYNKBS4HCZ6 \
  | 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: 9a5c93ab2908f05cbd8ec3541970e2cfaee14919a9a146ea1a3dd86567f696ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aab373131535a5eb892dd748f4205eb1e4b5d96bfea1ca1c53268dcdc47dd083",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2005-08-15T22:36:16Z",
    "title_canon_sha256": "675eb421d194809ac6038b48fe20e6f7bbe0ffbe47c912504cee535e06e378e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508270",
    "kind": "arxiv",
    "version": 2
  }
}