Pith Number

pith:LWF2NNXY

pith:2013:LWF2NNXYRFXNSJMB5WZSX4F5XZ

not attested not anchored not stored refs pending

A metric characterization of Carnot groups

Enrico Le Donne

arxiv:1304.7493 v2 · 2013-04-28 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LWF2NNXYRFXNSJMB5WZSX4F5XZ}

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	2026-05-18T02:44:32.309141Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d8ba6b6f8896ed92581edb32bf0bdbe791f2f9c514048b9763886217178bbb4

Aliases

arxiv: 1304.7493 · arxiv_version: 1304.7493v2 · doi: 10.48550/arxiv.1304.7493 · pith_short_12: LWF2NNXYRFXN · pith_short_16: LWF2NNXYRFXNSJMB · pith_short_8: LWF2NNXY

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/LWF2NNXYRFXNSJMB5WZSX4F5XZ \
  | 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: 5d8ba6b6f8896ed92581edb32bf0bdbe791f2f9c514048b9763886217178bbb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04fa6704f5ae97be239eff264dcb28e4f7ae2310b972afa5cbe14d7244620f4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-04-28T18:22:39Z",
    "title_canon_sha256": "f4a2588e30ec5d4837083cb76b82909d081bdaaea554910f51b179682f1d610c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.7493",
    "kind": "arxiv",
    "version": 2
  }
}