Pith Number

pith:OR5F5Z3P

pith:2015:OR5F5Z3PUYDEFZOQ7I3T2UWFLQ

not attested not anchored not stored refs pending

Sard Property for the endpoint map on some Carnot groups

Alessandro Ottazzi, Davide Vittone, Enrico Le Donne, Pierre Pansu, Richard Montgomery

arxiv:1503.03610 v1 · 2015-03-12 · math.DG · math.GR · math.MG · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OR5F5Z3PUYDEFZOQ7I3T2UWFLQ}

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	2026-05-18T00:54:41.714213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

747a5ee76fa60642e5d0fa373d52c55c1fe09ad5d9a70847acce258fffbfd89f

Aliases

arxiv: 1503.03610 · arxiv_version: 1503.03610v1 · doi: 10.48550/arxiv.1503.03610 · pith_short_12: OR5F5Z3PUYDE · pith_short_16: OR5F5Z3PUYDEFZOQ · pith_short_8: OR5F5Z3P

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/OR5F5Z3PUYDEFZOQ7I3T2UWFLQ \
  | 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: 747a5ee76fa60642e5d0fa373d52c55c1fe09ad5d9a70847acce258fffbfd89f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00e0168b3eab4388ca559dc1bb9fe7cefca86f434849c61595d1fac1d32f2ac3",
    "cross_cats_sorted": [
      "math.GR",
      "math.MG",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-03-12T07:10:13Z",
    "title_canon_sha256": "67533fc75f1fcc513c571474c0af11b4a6cfa7a4f0c13a37200e5f17ae3e4a59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.03610",
    "kind": "arxiv",
    "version": 1
  }
}