Pith Number

pith:A2RDI7GK

pith:2011:A2RDI7GKDPSZGEDDLO6E3AZ66D

not attested not anchored not stored refs pending

Commutativity pattern of finite non-abelian $p$-groups determine their orders

A. Abdollahi, H. Dorbidi, H. Shahverdi, S. Akbari

arxiv:1109.5007 v1 · 2011-09-23 · 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{A2RDI7GKDPSZGEDDLO6E3AZ66D}

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	2026-05-18T04:12:31.730512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06a2347cca1be59310635bbc4d833ef0e2ddfe95ef02a054d7d977470c5c97e2

Aliases

arxiv: 1109.5007 · arxiv_version: 1109.5007v1 · doi: 10.48550/arxiv.1109.5007 · pith_short_12: A2RDI7GKDPSZ · pith_short_16: A2RDI7GKDPSZGEDD · pith_short_8: A2RDI7GK

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/A2RDI7GKDPSZGEDDLO6E3AZ66D \
  | 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: 06a2347cca1be59310635bbc4d833ef0e2ddfe95ef02a054d7d977470c5c97e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "994cab2d64b6a1ac7989bff23b6e26b0717eadc6e25531e9c612a632a1209a1b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-09-23T06:48:35Z",
    "title_canon_sha256": "f2f1ab428c2198747a0e3f622b00a93a981e6ac682ef37524a86365503b68880"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5007",
    "kind": "arxiv",
    "version": 1
  }
}