Pith Number

pith:DMR7PTA5

pith:2015:DMR7PTA5IK32IRCB6LWXPGRHTJ

not attested not anchored not stored refs pending

Multiplication formulas in Moufang loops

Alexander N. Grishkov, Andrei V. Zavarnitsine

arxiv:1507.05262 v1 · 2015-07-19 · 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{DMR7PTA5IK32IRCB6LWXPGRHTJ}

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	2026-05-18T01:12:13.385182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b23f7cc1d42b7a44441f2ed779a279a7bcd314fb3a624d187760b977429a5a6

Aliases

arxiv: 1507.05262 · arxiv_version: 1507.05262v1 · doi: 10.48550/arxiv.1507.05262 · pith_short_12: DMR7PTA5IK32 · pith_short_16: DMR7PTA5IK32IRCB · pith_short_8: DMR7PTA5

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/DMR7PTA5IK32IRCB6LWXPGRHTJ \
  | 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: 1b23f7cc1d42b7a44441f2ed779a279a7bcd314fb3a624d187760b977429a5a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e54a571f8e31d7e3d0d27576312040e1e18109a66d23d91b2d0bb32b180a8de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-07-19T08:26:47Z",
    "title_canon_sha256": "8c9caaeab3909abd61f79d8037104433eb4d575847dacfce8e98dd688eb42f85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05262",
    "kind": "arxiv",
    "version": 1
  }
}