Pith Number

pith:OG6XXZOF

pith:2012:OG6XXZOF7XSB5RQECAKQRKK4IH

not attested not anchored not stored refs pending

Volume and distance comparison theorems for sub-Riemannian manifolds

Fabrice Baudoin, Isidro H. Munive, Michel Bonnefont, Nicola Garofalo

arxiv:1211.0221 v3 · 2012-11-01 · math.DG · 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{OG6XXZOF7XSB5RQECAKQRKK4IH}

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	2026-05-18T02:46:15.208976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71bd7be5c5fde41ec604101508a95c41c43cfabc422cfd1f0e273954cbf64655

Aliases

arxiv: 1211.0221 · arxiv_version: 1211.0221v3 · doi: 10.48550/arxiv.1211.0221 · pith_short_12: OG6XXZOF7XSB · pith_short_16: OG6XXZOF7XSB5RQE · pith_short_8: OG6XXZOF

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/OG6XXZOF7XSB5RQECAKQRKK4IH \
  | 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: 71bd7be5c5fde41ec604101508a95c41c43cfabc422cfd1f0e273954cbf64655

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c29d6a1e49906073962a89d9e9e9431349b24c91e467ed95d4021f654f5c8ff",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-11-01T16:44:28Z",
    "title_canon_sha256": "eea032f7e14becd044ed804f0ba7114dc0d82c0af4f98f2e9bf837643fc4a2d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0221",
    "kind": "arxiv",
    "version": 3
  }
}