Pith Number

pith:WUX62A2U

pith:2013:WUX62A2UV2W7YZ62WQ3OMELGQV

not attested not anchored not stored refs pending

$p$-Groups for which each outer $p$-automorphism centralizes only $p$ elements

Alireza Abdollahi, S. Mohsen Ghoraishi

arxiv:1307.5417 v1 · 2013-07-20 · 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{WUX62A2UV2W7YZ62WQ3OMELGQV}

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	2026-05-18T03:17:55.841181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b52fed0354aeadfc67dab436e61166854393a975933138dea89d8fe6010d1866

Aliases

arxiv: 1307.5417 · arxiv_version: 1307.5417v1 · doi: 10.48550/arxiv.1307.5417 · pith_short_12: WUX62A2UV2W7 · pith_short_16: WUX62A2UV2W7YZ62 · pith_short_8: WUX62A2U

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/WUX62A2UV2W7YZ62WQ3OMELGQV \
  | 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: b52fed0354aeadfc67dab436e61166854393a975933138dea89d8fe6010d1866

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1c13c30a7c1f618d24936d5167bd9acc84530d0bd89d527c509529fbbe5922d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-07-20T12:33:27Z",
    "title_canon_sha256": "04d5fc2e9d6b4e83a03410587e38b3efa20dd0df88cf8c52fd901a857945b23a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5417",
    "kind": "arxiv",
    "version": 1
  }
}