Pith Number

pith:URJWRPAH

pith:2016:URJWRPAHUAG5L7JOUAFSFIJBBB

not attested not anchored not stored refs pending

A primer on Carnot groups: homogenous groups, CC spaces, and regularity of their isometries

Enrico Le Donne

arxiv:1604.08579 v1 · 2016-04-28 · math.MG · math.DG · 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{URJWRPAHUAG5L7JOUAFSFIJBBB}

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	2026-05-18T01:16:03.630886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a45368bc07a00dd5fd2ea00b22a12108600ef5827a058b1e703bea17b1b1fc80

Aliases

arxiv: 1604.08579 · arxiv_version: 1604.08579v1 · doi: 10.48550/arxiv.1604.08579 · pith_short_12: URJWRPAHUAG5 · pith_short_16: URJWRPAHUAG5L7JO · pith_short_8: URJWRPAH

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/URJWRPAHUAG5L7JOUAFSFIJBBB \
  | 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: a45368bc07a00dd5fd2ea00b22a12108600ef5827a058b1e703bea17b1b1fc80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2640fad93f516f1d0a33994d0858296227b73fa7a10881ee329cef359f36df90",
    "cross_cats_sorted": [
      "math.DG",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-04-28T19:53:45Z",
    "title_canon_sha256": "63785cef74ae4dea273f5772643d942c3b8e8dddc0fe9ec1f960cf5a0b5417cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.08579",
    "kind": "arxiv",
    "version": 1
  }
}