Pith Number

pith:LW2JK5S4

pith:2012:LW2JK5S4R5PABHLRFMVDZGI7CH

not attested not anchored not stored refs pending

On embeddings into compactly generated groups

Pierre-Emmanuel Caprace, Yves Cornulier

arxiv:1211.5509 v1 · 2012-11-23 · 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{LW2JK5S4R5PABHLRFMVDZGI7CH}

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	2026-05-18T02:44:32.486494Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5db495765c8f5e009d712b2a3c991f11d705b13550f72abbd7455ddd60515bf8

Aliases

arxiv: 1211.5509 · arxiv_version: 1211.5509v1 · doi: 10.48550/arxiv.1211.5509 · pith_short_12: LW2JK5S4R5PA · pith_short_16: LW2JK5S4R5PABHLR · pith_short_8: LW2JK5S4

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/LW2JK5S4R5PABHLRFMVDZGI7CH \
  | 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: 5db495765c8f5e009d712b2a3c991f11d705b13550f72abbd7455ddd60515bf8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e851766a855089d15b8c57b545439248ff9ed2faf154514dff5a1f3f76b975e6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-11-23T13:57:59Z",
    "title_canon_sha256": "80a8e60f9a1d29e1a8bd64f508fcc0cdb172aca8799d253d869bf501f329b7b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5509",
    "kind": "arxiv",
    "version": 1
  }
}