Pith Number

pith:JR326HDA

pith:2015:JR326HDA2HZPEOOWYHYIB4HMEW

not attested not anchored not stored refs pending

Lamplighter groups, de Bruijn graphs, spider-web graphs and their spectra

Paul-Henry Leemann, Rostislav Grigorchuk, Tatiana Nagnibeda

arxiv:1502.06722 v3 · 2015-02-24 · math.CO · cond-mat.stat-mech · math-ph · math.GR · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JR326HDA2HZPEOOWYHYIB4HMEW}

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	2026-05-18T00:43:36.161812Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c77af1c60d1f2f239d6c1f080f0ec25be49d2dbe1e07b2057735272b29b80ec

Aliases

arxiv: 1502.06722 · arxiv_version: 1502.06722v3 · doi: 10.48550/arxiv.1502.06722 · pith_short_12: JR326HDA2HZP · pith_short_16: JR326HDA2HZPEOOW · pith_short_8: JR326HDA

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/JR326HDA2HZPEOOWYHYIB4HMEW \
  | 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: 4c77af1c60d1f2f239d6c1f080f0ec25be49d2dbe1e07b2057735272b29b80ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "049f437ee8b0283db2ad61db2dd6c0bc5aca2240c6c62bbffab656ed69973b44",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.GR",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-02-24T09:20:54Z",
    "title_canon_sha256": "bd03031d8be8c43d0c94e9a5d831e001868ced9f0c7c461b1bdac87fc50de860"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.06722",
    "kind": "arxiv",
    "version": 3
  }
}