Pith Number

pith:4BKKTMKX

pith:2011:4BKKTMKXZJKBLKTN7HUN6U5YHX

not attested not anchored not stored refs pending

Centralizers of coprime automorphisms of finite groups

Cristina Acciarri, Pavel Shumyatsky

arxiv:1112.5880 v1 · 2011-12-26 · 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{4BKKTMKXZJKBLKTN7HUN6U5YHX}

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	2026-05-18T04:05:37.364968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e054a9b157ca5415aa6df9e8df53b83dd3a8fbfbc3dae21be3ce312a9bd4bc8e

Aliases

arxiv: 1112.5880 · arxiv_version: 1112.5880v1 · doi: 10.48550/arxiv.1112.5880 · pith_short_12: 4BKKTMKXZJKB · pith_short_16: 4BKKTMKXZJKBLKTN · pith_short_8: 4BKKTMKX

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/4BKKTMKXZJKBLKTN7HUN6U5YHX \
  | 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: e054a9b157ca5415aa6df9e8df53b83dd3a8fbfbc3dae21be3ce312a9bd4bc8e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27bbbe50cc8b9f5687c5888ee3e974f9f335dac125bec3b69b682fbb74db4d65",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-12-26T18:52:08Z",
    "title_canon_sha256": "2fd55c6d055a60b989e00a7b0b824ed94c318b979d82e01700ac46503bb5cc58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5880",
    "kind": "arxiv",
    "version": 1
  }
}