Pith Number

pith:J73UIK4K

pith:2013:J73UIK4KTSDXBMHYRI4TLWCA2R

not attested not anchored not stored refs pending

Hardy-Sobolev inequalities for vector fields and canceling linear differential operators

Jean Van Schaftingen, Pierre Bousquet

arxiv:1305.4262 v2 · 2013-05-18 · 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{J73UIK4KTSDXBMHYRI4TLWCA2R}

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	2026-05-17T23:48:57.568064Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ff7442b8a9c8770b0f88a3935d840d44a6a39edafaca020344a3ac697e43445

Aliases

arxiv: 1305.4262 · arxiv_version: 1305.4262v2 · doi: 10.48550/arxiv.1305.4262 · pith_short_12: J73UIK4KTSDX · pith_short_16: J73UIK4KTSDXBMHY · pith_short_8: J73UIK4K

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/J73UIK4KTSDXBMHYRI4TLWCA2R \
  | 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: 4ff7442b8a9c8770b0f88a3935d840d44a6a39edafaca020344a3ac697e43445

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d375fb5d226f98f5ed1388657cdfc37137b87828aff5f12bbf51d65aa21be9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-05-18T13:19:47Z",
    "title_canon_sha256": "e1b54eb43bc619070737bc8a398fa7c5719e9fad48faf556d2b3c6480492d6ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.4262",
    "kind": "arxiv",
    "version": 2
  }
}