Pith Number

pith:B7HH7IEL

pith:2007:B7HH7IELCJNK6EJBNR4DENR42V

not attested not anchored not stored refs pending

On the spectrum of lamplighter groups and percolation clusters

Franz Lehner, Markus Neuhauser, Wolfgang Woess

arxiv:0712.3135 v2 · 2007-12-19 · math.FA · 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{B7HH7IELCJNK6EJBNR4DENR42V}

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	2026-05-18T03:39:14.943203Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fce7fa08b125aaf11216c7832363cd57130ac15acc29e00cfcbc39744b9e48e

Aliases

arxiv: 0712.3135 · arxiv_version: 0712.3135v2 · doi: 10.48550/arxiv.0712.3135 · pith_short_12: B7HH7IELCJNK · pith_short_16: B7HH7IELCJNK6EJB · pith_short_8: B7HH7IEL

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/B7HH7IELCJNK6EJBNR4DENR42V \
  | 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: 0fce7fa08b125aaf11216c7832363cd57130ac15acc29e00cfcbc39744b9e48e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c706eae6d7130e20a955340246cb26d51a2566637198aad079d578f08a607871",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2007-12-19T10:00:31Z",
    "title_canon_sha256": "f2ec5de4fc84637a85c4d672487982ea2173efcbebdf9a44b7f6bc7962c9b16f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3135",
    "kind": "arxiv",
    "version": 2
  }
}