Pith Number

pith:ZOVVDR4L

pith:2019:ZOVVDR4LI72NNX4JZ2M25C45OM

not attested not anchored not stored refs pending

A simple proof of the Hardy inequality on Carnot groups and for some hypoelliptic families of vector fields

Fran\c{c}ois Vigneron (LAMA)

arxiv:1908.06728 v1 · 2019-08-19 · math.CA · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZOVVDR4LI72NNX4JZ2M25C45OM}

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	2026-07-05T00:26:39.787538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbab51c78b47f4d6df89ce99ae8b9d7322b937b77e6a3475d07bb9d788839426

Aliases

arxiv: 1908.06728 · arxiv_version: 1908.06728v1 · doi: 10.48550/arxiv.1908.06728 · pith_short_12: ZOVVDR4LI72N · pith_short_16: ZOVVDR4LI72NNX4J · pith_short_8: ZOVVDR4L

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/ZOVVDR4LI72NNX4JZ2M25C45OM \
  | 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: cbab51c78b47f4d6df89ce99ae8b9d7322b937b77e6a3475d07bb9d788839426

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0491da0334aa6a2b652a7a49f26f53cc9caf245d0a68d9bf90dcd1d8496d685",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-08-19T12:21:12Z",
    "title_canon_sha256": "727b379fff41ab817c4e0fdb863fcfe67ee8657bf44b399a0c903ec75268c463"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.06728",
    "kind": "arxiv",
    "version": 1
  }
}