Pith Number

pith:Q4JC2KR7

pith:2022:Q4JC2KR7VS6BSMKZ6JIR22RQRB

not attested not anchored not stored refs pending

A classification of finite $p$-groups with a unique $\mathcal{A}_2$-subgroup

Dandan Zhang, Haipeng Qu, Jixia Gao

arxiv:2203.07592 v1 · 2022-03-15 · 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{Q4JC2KR7VS6BSMKZ6JIR22RQRB}

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	2026-07-05T04:05:20.283830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87122d2a3facbc193159f2511d6a30886114f4a0ca2f7eb27cc649a5a1c9719e

Aliases

arxiv: 2203.07592 · arxiv_version: 2203.07592v1 · doi: 10.48550/arxiv.2203.07592 · pith_short_12: Q4JC2KR7VS6B · pith_short_16: Q4JC2KR7VS6BSMKZ · pith_short_8: Q4JC2KR7

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/Q4JC2KR7VS6BSMKZ6JIR22RQRB \
  | 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: 87122d2a3facbc193159f2511d6a30886114f4a0ca2f7eb27cc649a5a1c9719e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a17117d4228e549349e8035c315cc56d6ca691dbe7ff6f56fda3c7ac4df1181b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2022-03-15T01:41:52Z",
    "title_canon_sha256": "a294046fff6ac60d6755ea3e612ce0aedcffdbdc1d802d0eef4c049fb69ec8f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.07592",
    "kind": "arxiv",
    "version": 1
  }
}