Pith Number

pith:56Z4XHU7

pith:2008:56Z4XHU7IWOMP4ZXJPLSODF3IK

not attested not anchored not stored refs pending

Replica overlap and covering time for the Wiener sausages among Poissonian obstacles

Ryoki Fukushima

arxiv:0809.0262 v1 · 2008-09-01 · 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{56Z4XHU7IWOMP4ZXJPLSODF3IK}

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	2026-05-17T23:41:31.684547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efb3cb9e9f459cc7f3374bd7270cbb42bce1da8ab614d6efd48f58edfa6e7ebf

Aliases

arxiv: 0809.0262 · arxiv_version: 0809.0262v1 · doi: 10.48550/arxiv.0809.0262 · pith_short_12: 56Z4XHU7IWOM · pith_short_16: 56Z4XHU7IWOMP4ZX · pith_short_8: 56Z4XHU7

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/56Z4XHU7IWOMP4ZXJPLSODF3IK \
  | 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: efb3cb9e9f459cc7f3374bd7270cbb42bce1da8ab614d6efd48f58edfa6e7ebf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c24fdd35e634e6701aacc97d9339b36e40ecc1a03ce134eba060264b97526991",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-09-01T15:06:04Z",
    "title_canon_sha256": "a7631e19ab217ccb7ac0f1f523a1be540e24cad1526a840c28cc7c751aa01fca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.0262",
    "kind": "arxiv",
    "version": 1
  }
}