Pith Number

pith:IPGQDGUM

pith:2006:IPGQDGUMTUDI46BIZ5QXM3DNXN

not attested not anchored not stored refs pending

Tug-of-war and the infinity Laplacian

David B. Wilson, Oded Schramm, Scott Sheffield, Yuval Peres

arxiv:math/0605002 v2 · 2006-04-28 · math.AP · math.MG · math.OC · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IPGQDGUMTUDI46BIZ5QXM3DNXN}

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	2026-05-18T03:53:07.393614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43cd019a8c9d068e7828cf61766c6dbb59c542a9a4787d10ea517c39f6999728

Aliases

arxiv: math/0605002 · arxiv_version: math/0605002v2 · doi: 10.48550/arxiv.math/0605002 · pith_short_12: IPGQDGUMTUDI · pith_short_16: IPGQDGUMTUDI46BI · pith_short_8: IPGQDGUM

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/IPGQDGUMTUDI46BIZ5QXM3DNXN \
  | 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: 43cd019a8c9d068e7828cf61766c6dbb59c542a9a4787d10ea517c39f6999728

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71bcf9b69ed405501cda2f7626418868691b9105b1cd9b2ab1c6608794cc11fd",
    "cross_cats_sorted": [
      "math.MG",
      "math.OC",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2006-04-28T21:42:00Z",
    "title_canon_sha256": "61c0d3535681235b89abb604a2960dd768b988ebfa28e8612097d6632e70ec79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0605002",
    "kind": "arxiv",
    "version": 2
  }
}