Pith Number

pith:L4NRAX3Y

pith:2013:L4NRAX3YK5NTJRIXC57XVHCBOT

not attested not anchored not stored refs pending

Rationality of the probabilistic zeta function of finitely generated profinite groups

Andrea Lucchini, Duong Hoang Dung

arxiv:1301.3830 v2 · 2013-01-16 · 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{L4NRAX3YK5NTJRIXC57XVHCBOT}

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	2026-05-18T03:04:59.606969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f1b105f78575b34c517177f7a9c4174df3633ffdd4b2a2fbcd6a714b3cac3be

Aliases

arxiv: 1301.3830 · arxiv_version: 1301.3830v2 · doi: 10.48550/arxiv.1301.3830 · pith_short_12: L4NRAX3YK5NT · pith_short_16: L4NRAX3YK5NTJRIX · pith_short_8: L4NRAX3Y

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/L4NRAX3YK5NTJRIXC57XVHCBOT \
  | 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: 5f1b105f78575b34c517177f7a9c4174df3633ffdd4b2a2fbcd6a714b3cac3be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "054020269c93872b19e031e411fb1ef894bcf1b6015dbc57e34c2b70f2548a34",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-01-16T10:05:22Z",
    "title_canon_sha256": "23d9dee63fd56c7d118e3e2f2c6d8594c0f5afbe5cab657a3ef8867e20e65d23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.3830",
    "kind": "arxiv",
    "version": 2
  }
}