Pith Number

pith:6GM6DPUT

pith:2013:6GM6DPUTSQ4LC5UFU5FULQMPWX

not attested not anchored not stored refs pending

Groups with infinitely many ends are not fraction groups

Dawid Kielak

arxiv:1303.1656 v2 · 2013-03-07 · 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{6GM6DPUTSQ4LC5UFU5FULQMPWX}

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	2026-05-18T01:56:00.149448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f199e1be939438b17685a74b45c18fb5e15c354bcad1ee56c0201a37427358c1

Aliases

arxiv: 1303.1656 · arxiv_version: 1303.1656v2 · doi: 10.48550/arxiv.1303.1656 · pith_short_12: 6GM6DPUTSQ4L · pith_short_16: 6GM6DPUTSQ4LC5UF · pith_short_8: 6GM6DPUT

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/6GM6DPUTSQ4LC5UFU5FULQMPWX \
  | 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: f199e1be939438b17685a74b45c18fb5e15c354bcad1ee56c0201a37427358c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9a7f1f9a085bef73863a476f4c147a53a1cdcc5f013dbdd6a5149649d656ed5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-03-07T12:09:11Z",
    "title_canon_sha256": "9f76bc944b9fc209cf36b71a7f930c403affbef5e002a69fce43bb49e1e31469"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.1656",
    "kind": "arxiv",
    "version": 2
  }
}