Pith Number

pith:MGQCA3MX

pith:2015:MGQCA3MXMYWP27AYUG5PEH7BCY

not attested not anchored not stored refs pending

Closest multiplication tables of groups

Ian M. Wanless, Petr Vojt\v{e}chovsk\'y

arxiv:1509.05660 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{MGQCA3MXMYWP27AYUG5PEH7BCY}

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	2026-05-18T01:32:42.666262Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61a0206d97662cfd7c18a1baf21fe1161197f630cae6eba224f8b6ba07e5b474

Aliases

arxiv: 1509.05660 · arxiv_version: 1509.05660v1 · doi: 10.48550/arxiv.1509.05660 · pith_short_12: MGQCA3MXMYWP · pith_short_16: MGQCA3MXMYWP27AY · pith_short_8: MGQCA3MX

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/MGQCA3MXMYWP27AYUG5PEH7BCY \
  | 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: 61a0206d97662cfd7c18a1baf21fe1161197f630cae6eba224f8b6ba07e5b474

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db458bb3afaf8f7436025804bbc04a930836ad3d06a41ac9a5922460abe63515",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-18T15:22:07Z",
    "title_canon_sha256": "c3cdd646f141dd3250d5dc87e704998db2558eeb0be1b29a83d481db5b5142ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05660",
    "kind": "arxiv",
    "version": 1
  }
}