Pith Number

pith:MYTDYW3U

pith:2009:MYTDYW3UHIMNFAJUJL7ZHQXPRC

not attested not anchored not stored refs pending

Lamplighter graphs do not admit harmonic functions of finite energy

Agelos Georgakopoulos

arxiv:0907.1398 v2 · 2009-07-08 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MYTDYW3UHIMNFAJUJL7ZHQXPRC}

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	2026-07-04T15:46:13.355993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66263c5b743a18d281344aff93c2ef888e0ccdd4964644bf2ab093408fe65af0

Aliases

arxiv: 0907.1398 · arxiv_version: 0907.1398v2 · doi: 10.48550/arxiv.0907.1398 · pith_short_12: MYTDYW3UHIMN · pith_short_16: MYTDYW3UHIMNFAJU · pith_short_8: MYTDYW3U

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/MYTDYW3UHIMNFAJUJL7ZHQXPRC \
  | 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: 66263c5b743a18d281344aff93c2ef888e0ccdd4964644bf2ab093408fe65af0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "080672ebe523714ef0eb31414a0a9298d2aa1d99e9671a255cae74e5c4e85c3a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-07-08T12:19:12Z",
    "title_canon_sha256": "6539a20e51bb78b98f06fbe4242cc5b6339f7587eee1064f4fddf1d583b442b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.1398",
    "kind": "arxiv",
    "version": 2
  }
}