Pith Number

pith:NKHQDH6N

pith:2013:NKHQDH6NBPDHAUIA5QMRNU3FMK

not attested not anchored not stored refs pending

Finite p-groups with central automorphism group of minimal order

Deepak Gumber, Hemant Kalra

arxiv:1305.6440 v1 · 2013-05-28 · 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{NKHQDH6NBPDHAUIA5QMRNU3FMK}

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	2026-05-18T02:23:35.503356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a8f019fcd0bc6705100ec1916d365629922383922cde490641a4784ece8b788

Aliases

arxiv: 1305.6440 · arxiv_version: 1305.6440v1 · doi: 10.48550/arxiv.1305.6440 · pith_short_12: NKHQDH6NBPDH · pith_short_16: NKHQDH6NBPDHAUIA · pith_short_8: NKHQDH6N

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/NKHQDH6NBPDHAUIA5QMRNU3FMK \
  | 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: 6a8f019fcd0bc6705100ec1916d365629922383922cde490641a4784ece8b788

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "251b2529a5b528375278add043862789c25f23b3830ca1cc642818670d9a8f91",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-05-28T10:31:34Z",
    "title_canon_sha256": "c0196de87114e6dbe376cc3e0f83ac5a5dd55c6a81ac4cde647a42df8c31fb61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.6440",
    "kind": "arxiv",
    "version": 1
  }
}