Pith Number

pith:WNHCZAQP

pith:2004:WNHCZAQP2R5LIBLQ6BECQ2GISY

not attested not anchored not stored refs pending

Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel-Leader graphs

Sara Brofferio, Wolfgang Woess

arxiv:math/0403267 v1 · 2004-03-16 · 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{WNHCZAQP2R5LIBLQ6BECQ2GISY}

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	2026-05-18T01:38:28.490849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b34e2c820fd47ab40570f0482868c89621eaa547295cac9dc81da9dc75100334

Aliases

arxiv: math/0403267 · arxiv_version: math/0403267v1 · doi: 10.48550/arxiv.math/0403267 · pith_short_12: WNHCZAQP2R5L · pith_short_16: WNHCZAQP2R5LIBLQ · pith_short_8: WNHCZAQP

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/WNHCZAQP2R5LIBLQ6BECQ2GISY \
  | 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: b34e2c820fd47ab40570f0482868c89621eaa547295cac9dc81da9dc75100334

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49347de0204c09115157debea9cfbbabe37e718bad8870c992692d8fc01135b1",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-03-16T15:34:12Z",
    "title_canon_sha256": "92f4c45482776cc55638cdd31dcda606b598fd52dea7d4f56d3fec465c3282dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0403267",
    "kind": "arxiv",
    "version": 1
  }
}