Pith Number

pith:QPJCMK3N

pith:2012:QPJCMK3NZMNJSN23ZWGJN2I553

not attested not anchored not stored refs pending

The Brin-Thompson groups sV are of type F_\infty

Marco Marschler, Martin Fluch, Matthew C. B. Zaremsky, Stefan Witzel

arxiv:1207.4832 v3 · 2012-07-20 · math.GR · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QPJCMK3NZMNJSN23ZWGJN2I553}

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	2026-05-18T02:56:11.794444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83d2262b6dcb1a99375bcd8c96e91deee13ad8671dad19ebec66fc6c714d47e3

Aliases

arxiv: 1207.4832 · arxiv_version: 1207.4832v3 · doi: 10.48550/arxiv.1207.4832 · pith_short_12: QPJCMK3NZMNJ · pith_short_16: QPJCMK3NZMNJSN23 · pith_short_8: QPJCMK3N

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/QPJCMK3NZMNJSN23ZWGJN2I553 \
  | 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: 83d2262b6dcb1a99375bcd8c96e91deee13ad8671dad19ebec66fc6c714d47e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7fbbf4c7df4e79ff461d3adb344696bcc42fa3a1158de7088bbfdde89ee2ea4",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-07-20T00:15:14Z",
    "title_canon_sha256": "213afa693aa4029e4725659467dcfb1cf766b63002e25f86591d45a84c95d398"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4832",
    "kind": "arxiv",
    "version": 3
  }
}