Pith Number

pith:OZ5RGM2O

pith:2011:OZ5RGM2OOBYORIRKJKFBFZ72SE

not attested not anchored not stored refs pending

On the exponent of a finite group admitting a fixed-point-free four-group of automorphisms

E. Romano, P. Shumyatsky

arxiv:1101.5367 v1 · 2011-01-27 · 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{OZ5RGM2OOBYORIRKJKFBFZ72SE}

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	2026-05-18T04:30:35.615694Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

767b13334e7070e8a22a4a8a12e7fa9109314de7184e77f21b4f060535aabb67

Aliases

arxiv: 1101.5367 · arxiv_version: 1101.5367v1 · doi: 10.48550/arxiv.1101.5367 · pith_short_12: OZ5RGM2OOBYO · pith_short_16: OZ5RGM2OOBYORIRK · pith_short_8: OZ5RGM2O

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/OZ5RGM2OOBYORIRKJKFBFZ72SE \
  | 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: 767b13334e7070e8a22a4a8a12e7fa9109314de7184e77f21b4f060535aabb67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61417d5c5f05a7e46b49a56369dccb2c11f1c9b3411b227df72b832ddb5d2064",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-01-27T19:23:54Z",
    "title_canon_sha256": "da85becea26372560265c7c3d9ba51b079e1720e4a3b930b622744bf52a2f876"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5367",
    "kind": "arxiv",
    "version": 1
  }
}