Pith Number

pith:5NSB57EH

pith:2013:5NSB57EHYPC27X2TUZPSZT2CY5

not attested not anchored not stored refs pending

New Examples of Torsion-Free Non-unique Product Groups

William Carter

arxiv:1302.0049 v4 · 2013-02-01 · 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{5NSB57EHYPC27X2TUZPSZT2CY5}

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	2026-05-18T03:06:22.271222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb641efc87c3c5afdf53a65f2ccf42c76c5d423ab5572a563d0aac7954ed2f06

Aliases

arxiv: 1302.0049 · arxiv_version: 1302.0049v4 · doi: 10.48550/arxiv.1302.0049 · pith_short_12: 5NSB57EHYPC2 · pith_short_16: 5NSB57EHYPC27X2T · pith_short_8: 5NSB57EH

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/5NSB57EHYPC27X2TUZPSZT2CY5 \
  | 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: eb641efc87c3c5afdf53a65f2ccf42c76c5d423ab5572a563d0aac7954ed2f06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed98bde3c50d6ed1aa03a1005fe0aa64678a3c8ae673fd884b93afa60d67a896",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-02-01T00:59:05Z",
    "title_canon_sha256": "297f5b22e9fd6bf419c4b81d0e33846b428ba5737c246a48731c403de03bc1df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.0049",
    "kind": "arxiv",
    "version": 4
  }
}