Pith Number

pith:V3SCG7RF

pith:2006:V3SCG7RFFDG7FWGR5EDCLKQ76H

not attested not anchored not stored refs pending

Giant Component and Vacant Set for Random Walk on a Discrete Torus

Alain-Sol Sznitman, Itai Benjamini

arxiv:math/0610802 v2 · 2006-10-26 · math.PR · math-ph · math.CO · 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{V3SCG7RFFDG7FWGR5EDCLKQ76H}

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	2026-05-18T04:08:53.163853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aee4237e2528cdf2d8d1e90625aa1ff1d785b812ee92383ada636f81193ae1bf

Aliases

arxiv: math/0610802 · arxiv_version: math/0610802v2 · doi: 10.48550/arxiv.math/0610802 · pith_short_12: V3SCG7RFFDG7 · pith_short_16: V3SCG7RFFDG7FWGR · pith_short_8: V3SCG7RF

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/V3SCG7RFFDG7FWGR5EDCLKQ76H \
  | 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: aee4237e2528cdf2d8d1e90625aa1ff1d785b812ee92383ada636f81193ae1bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "551f95369f08e98fd0d43081388a331ffb357ad2fddaaba71c442c638af9470f",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2006-10-26T17:10:26Z",
    "title_canon_sha256": "d04d198ebe6a37154c7af9ee5044c21c71a4cfa280d2ea0ff17db6d3e3c4d855"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0610802",
    "kind": "arxiv",
    "version": 2
  }
}