Pith Number

pith:N6UMSPYW

pith:2009:N6UMSPYW6QYG5NEQWAAPLUTH3S

not attested not anchored not stored refs pending

C$^*$-simple groups: amalgamated free products, HNN extensions, and fundamental groups of 3-manifolds

Jean-Philippe Pr\'eaux, Pierre de la Harpe

arxiv:0909.3528 v2 · 2009-09-18 · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N6UMSPYW6QYG5NEQWAAPLUTH3S}

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	2026-05-18T04:01:00.201254Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fa8c93f16f4306eb490b000f5d267dcb6eb0eb21dab7080bc95366de22359d9

Aliases

arxiv: 0909.3528 · arxiv_version: 0909.3528v2 · doi: 10.48550/arxiv.0909.3528 · pith_short_12: N6UMSPYW6QYG · pith_short_16: N6UMSPYW6QYG5NEQ · pith_short_8: N6UMSPYW

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/N6UMSPYW6QYG5NEQWAAPLUTH3S \
  | 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: 6fa8c93f16f4306eb490b000f5d267dcb6eb0eb21dab7080bc95366de22359d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6a8e60f2b7feee3c696bdebc5035a90b80fe0a3848acb368693b49236f408c1",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-09-18T20:30:54Z",
    "title_canon_sha256": "2e32588794892adad34b7622754463c86516dc00c5f3ae6cfcba17daadd6e72f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.3528",
    "kind": "arxiv",
    "version": 2
  }
}