Pith Number

pith:YQCFOB2Q

pith:2006:YQCFOB2QPVWDNNNV2NHBHV6BA4

not attested not anchored not stored refs pending

The Poisson boundary of lamplighter random walks on trees

Anders Karlsson, Wolfgang Woess

arxiv:math/0606046 v1 · 2006-06-02 · 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{YQCFOB2QPVWDNNNV2NHBHV6BA4}

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	2026-05-18T03:39:14.959133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4045707507d6c36b5b5d34e13d7c107038927fd7743fd855e7fdbdabe78d3c6

Aliases

arxiv: math/0606046 · arxiv_version: math/0606046v1 · doi: 10.48550/arxiv.math/0606046 · pith_short_12: YQCFOB2QPVWD · pith_short_16: YQCFOB2QPVWDNNNV · pith_short_8: YQCFOB2Q

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/YQCFOB2QPVWDNNNV2NHBHV6BA4 \
  | 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: c4045707507d6c36b5b5d34e13d7c107038927fd7743fd855e7fdbdabe78d3c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a004f71052829a60d1bd2c7c3eb88ebebd54a6c5dc2d1f7a2aa2034091d25644",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2006-06-02T08:41:42Z",
    "title_canon_sha256": "00615710fade50654648e3462a23016d9dd15b58a11305a12dd55cc464ddefa6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0606046",
    "kind": "arxiv",
    "version": 1
  }
}