Pith Number

pith:JHOE7WDG

pith:2006:JHOE7WDGWQB7EHWUZVMFNBARPA

not attested not anchored not stored refs pending

Finite $p$-groups of class 2 have noninner automorphisms of order $p$

A. Abdollahi

arxiv:math/0608581 v1 · 2006-08-23 · 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{JHOE7WDGWQB7EHWUZVMFNBARPA}

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	2026-05-18T01:05:22.580577Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49dc4fd866b403f21ed4cd5856841178031280ff2407b88d17d7ddad91ed495a

Aliases

arxiv: math/0608581 · arxiv_version: math/0608581v1 · doi: 10.48550/arxiv.math/0608581 · pith_short_12: JHOE7WDGWQB7 · pith_short_16: JHOE7WDGWQB7EHWU · pith_short_8: JHOE7WDG

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/JHOE7WDGWQB7EHWUZVMFNBARPA \
  | 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: 49dc4fd866b403f21ed4cd5856841178031280ff2407b88d17d7ddad91ed495a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83e88ce63064388c9d56450ea756d6cee59e1b5dbfa19aa885d75d91362063bd",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2006-08-23T15:57:44Z",
    "title_canon_sha256": "7f72e89012a2fc524da13c1b0f7f74f43f5cc113b9c12f79bc35867634227eb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0608581",
    "kind": "arxiv",
    "version": 1
  }
}