Pith Number

pith:5YK6TAK3

pith:2009:5YK6TAK3IRWI7C4TOMGWIK6Z6I

not attested not anchored not stored refs pending

Commensurators of non-free finitely generated Kleinian groups

A. W. Reid, C. J. Leininger, D. D. Long

arxiv:0908.2272 v1 · 2009-08-17 · math.GT · 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{5YK6TAK3IRWI7C4TOMGWIK6Z6I}

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	2026-05-18T02:41:51.183988Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee15e9815b446c8f8b93730d642bd9f23cad1384eb7d502fae1b95615e482c55

Aliases

arxiv: 0908.2272 · arxiv_version: 0908.2272v1 · doi: 10.48550/arxiv.0908.2272 · pith_short_12: 5YK6TAK3IRWI · pith_short_16: 5YK6TAK3IRWI7C4T · pith_short_8: 5YK6TAK3

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/5YK6TAK3IRWI7C4TOMGWIK6Z6I \
  | 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: ee15e9815b446c8f8b93730d642bd9f23cad1384eb7d502fae1b95615e482c55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bebd2c6bcd4ae55993e67d88b1612c434072d3a19e5cabdfefd60a9aac5ef6a5",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-08-17T01:59:43Z",
    "title_canon_sha256": "3cfdff26236b09335b56637353aafd358cd18d10ad188f483770179cde39697b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.2272",
    "kind": "arxiv",
    "version": 1
  }
}