Pith Number

pith:57TQK7ZK

pith:2015:57TQK7ZKJJW3P6KALG4E7F4X5D

not attested not anchored not stored refs pending

Commutative automorphic loops of order $p^3$

Alexander Grishkov, Dylene Agda Souza de Barros, Petr Vojt\v{e}chovsk\'y

arxiv:1509.05727 v1 · 2015-09-18 · 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{57TQK7ZKJJW3P6KALG4E7F4X5D}

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	2026-05-18T01:32:42.501910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efe7057f2a4a6db7f94059b84f9797e8dbcfb4a27ac32b8ec0461b51d6e71183

Aliases

arxiv: 1509.05727 · arxiv_version: 1509.05727v1 · doi: 10.48550/arxiv.1509.05727 · pith_short_12: 57TQK7ZKJJW3 · pith_short_16: 57TQK7ZKJJW3P6KA · pith_short_8: 57TQK7ZK

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/57TQK7ZKJJW3P6KALG4E7F4X5D \
  | 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: efe7057f2a4a6db7f94059b84f9797e8dbcfb4a27ac32b8ec0461b51d6e71183

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f9b1004e090ef20cc3f4cff9e2abc3aa1d95fef61e1a0609de73f9ba59a6942",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-18T17:44:37Z",
    "title_canon_sha256": "0ea132b03caa4cd6c68505c785791b74cb3665d89205f7e9d949a9b98a75d424"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05727",
    "kind": "arxiv",
    "version": 1
  }
}