Pith Number

pith:VTGLRPDT

pith:2003:VTGLRPDTAUQOEBE3AKF2TPQAIR

not attested not anchored not stored refs pending

Loop-erased random walk on a torus in dimensions 4 and above

Gady Kozma, Itai Benjamini

arxiv:math/0309009 v1 · 2003-08-31 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VTGLRPDTAUQOEBE3AKF2TPQAIR}

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	2026-07-04T14:37:41.128223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acccb8bc730520e2049b028ba9be00446216e94e5cf720f2f714895323af2e0d

Aliases

arxiv: math/0309009 · arxiv_version: math/0309009v1 · doi: 10.48550/arxiv.math/0309009 · pith_short_12: VTGLRPDTAUQO · pith_short_16: VTGLRPDTAUQOEBE3 · pith_short_8: VTGLRPDT

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/VTGLRPDTAUQOEBE3AKF2TPQAIR \
  | 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: acccb8bc730520e2049b028ba9be00446216e94e5cf720f2f714895323af2e0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c3de017dbbcc26492ac061b9a1534eb5c1dac3235fa61ea6e8cdfd02916b170",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2003-08-31T16:10:14Z",
    "title_canon_sha256": "9f487e616ae9a3f643c726c555ea122b9e92ac8c7da06889d13f1bfb757a6c40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0309009",
    "kind": "arxiv",
    "version": 1
  }
}