Pith Number

pith:XU3FIE7W

pith:2015:XU3FIE7WVTE2RSND4R6WY3NAG6

not attested not anchored not stored refs pending

The free commutative automorphic $2$-generated loop of nilpotency class $3$

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

arxiv:1509.05465 v1 · 2015-09-17 · 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{XU3FIE7WVTE2RSND4R6WY3NAG6}

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	2026-05-18T01:32:43.128741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd365413f6acc9a8c9a3e47d6c6da037bb900489ac0ec733a138a854f83e1b90

Aliases

arxiv: 1509.05465 · arxiv_version: 1509.05465v1 · doi: 10.48550/arxiv.1509.05465 · pith_short_12: XU3FIE7WVTE2 · pith_short_16: XU3FIE7WVTE2RSND · pith_short_8: XU3FIE7W

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/XU3FIE7WVTE2RSND4R6WY3NAG6 \
  | 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: bd365413f6acc9a8c9a3e47d6c6da037bb900489ac0ec733a138a854f83e1b90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5483d61c4635bd8f35a40b2b03ec769edf77ccda4f458050e6da7fb2550a30f1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-17T22:41:23Z",
    "title_canon_sha256": "8282f2f0fd2c60b06c5054262f930c190ba5e6d2a6efef21d17739cbdfe1e80c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05465",
    "kind": "arxiv",
    "version": 1
  }
}