Pith Number

pith:S4CNACOA

pith:2010:S4CNACOAR67YLJPDG3TWA5YW6R

not attested not anchored not stored refs pending

On the Hausdorff volume in sub-Riemannian geometry

Andrei Agrachev, Davide Barilari, Ugo Boscain

arxiv:1005.0540 v3 · 2010-05-04 · math.DG · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S4CNACOAR67YLJPDG3TWA5YW6R}

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	2026-05-18T03:40:49.808536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9704d009c08fbf85a5e336e7607716f47366b4e83f1402a79405df38250523cc

Aliases

arxiv: 1005.0540 · arxiv_version: 1005.0540v3 · doi: 10.48550/arxiv.1005.0540 · pith_short_12: S4CNACOAR67Y · pith_short_16: S4CNACOAR67YLJPD · pith_short_8: S4CNACOA

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/S4CNACOAR67YLJPDG3TWA5YW6R \
  | 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: 9704d009c08fbf85a5e336e7607716f47366b4e83f1402a79405df38250523cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "495daef3b63299a8f390a97bd36ddeed584c6a2485d057354724924387b79c60",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-05-04T14:29:54Z",
    "title_canon_sha256": "76e5d73a301e9b53d1027b780569f121d9964c625c2c7ad7e28d44d35e33d33a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.0540",
    "kind": "arxiv",
    "version": 3
  }
}