Pith Number

pith:HELSWPHT

pith:2004:HELSWPHTUOCJBZ52LVFGIY6Y5H

not attested not anchored not stored refs pending

Lamplighters, Diestel-Leader graphs, random walks, and harmonic functions

Wolfgang Woess

arxiv:math/0403320 v1 · 2004-03-19 · 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{HELSWPHTUOCJBZ52LVFGIY6Y5H}

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	2026-05-18T03:39:14.997993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39172b3cf3a38490e7ba5d4a6463d8e9ceb22b8cf65fd7ee293576a07b8d21da

Aliases

arxiv: math/0403320 · arxiv_version: math/0403320v1 · doi: 10.48550/arxiv.math/0403320 · pith_short_12: HELSWPHTUOCJ · pith_short_16: HELSWPHTUOCJBZ52 · pith_short_8: HELSWPHT

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/HELSWPHTUOCJBZ52LVFGIY6Y5H \
  | 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: 39172b3cf3a38490e7ba5d4a6463d8e9ceb22b8cf65fd7ee293576a07b8d21da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52bcbc738e7f3c399d81252f8818252eb1b6b02715a6b25aedd40a732e612095",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-03-19T14:30:18Z",
    "title_canon_sha256": "9186236b03a796d94b66e8fc17ff0b0773f9b2826f65565a49ccfde47304b3c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0403320",
    "kind": "arxiv",
    "version": 1
  }
}