Pith Number

pith:KUDL65HL

pith:2006:KUDL65HLSMZZZJIJQ4KCFKGY2E

not attested not anchored not stored refs pending

On the range of the simple random walk bridge on groups

Harry Kesten, Itai Benjamini, Roey Izkovsky

arxiv:math/0605050 v1 · 2006-05-02 · math.PR · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KUDL65HLSMZZZJIJQ4KCFKGY2E}

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	2026-07-04T14:55:01.671196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5506bf74eb93339ca509871422a8d8d124f822484aac319a54474b3e090085e0

Aliases

arxiv: math/0605050 · arxiv_version: math/0605050v1 · doi: 10.48550/arxiv.math/0605050 · pith_short_12: KUDL65HLSMZZ · pith_short_16: KUDL65HLSMZZZJIJ · pith_short_8: KUDL65HL

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/KUDL65HLSMZZZJIJQ4KCFKGY2E \
  | 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: 5506bf74eb93339ca509871422a8d8d124f822484aac319a54474b3e090085e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48c22ee9e8ed182173211634d22cedb84142d4d937033199a0d1553c7367b1c3",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2006-05-02T12:02:26Z",
    "title_canon_sha256": "5ab2cb7191c7bd932460c198fb765cbfc9d662982c28abb3fb380d792c533c97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0605050",
    "kind": "arxiv",
    "version": 1
  }
}