Pith Number

pith:6NCPVD7M

pith:2015:6NCPVD7MDB7KURBX5NLZQJLXNF

not attested not anchored not stored refs pending

Centralizers of Camina $p$-groups of nilpotence class $3$

Mark L. Lewis

arxiv:1510.06293 v2 · 2015-10-21 · 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{6NCPVD7MDB7KURBX5NLZQJLXNF}

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	2026-05-18T01:26:09.325116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f344fa8fec187eaa4437eb57982577694b22c2dc4623dab4ef6eb9bd3aba9766

Aliases

arxiv: 1510.06293 · arxiv_version: 1510.06293v2 · doi: 10.48550/arxiv.1510.06293 · pith_short_12: 6NCPVD7MDB7K · pith_short_16: 6NCPVD7MDB7KURBX · pith_short_8: 6NCPVD7M

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/6NCPVD7MDB7KURBX5NLZQJLXNF \
  | 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: f344fa8fec187eaa4437eb57982577694b22c2dc4623dab4ef6eb9bd3aba9766

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec3e8f606f3f0ca09ef22c06c51b6b4f31ec2756d52d21081d6f9ee6aed91674",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-10-21T15:14:22Z",
    "title_canon_sha256": "61ca1018202ffa99c5fcd117ca83bb4e94e958c268d3ef8781df8f487f22dcac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.06293",
    "kind": "arxiv",
    "version": 2
  }
}