Pith Number

pith:HL3NJBEF

pith:2018:HL3NJBEFQD6OFUCINT44MMBJGT

not attested not anchored not stored refs pending

Geometric Hardy and Hardy-Sobolev inequalities on Heisenberg groups

Bolys Sabitbek, Durvudkhan Suragan, Michael Ruzhansky

arxiv:1811.07181 v1 · 2018-11-17 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HL3NJBEFQD6OFUCINT44MMBJGT}

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	2026-05-18T00:00:28.700274Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3af6d4848580fce2d0486cf9c6302934d8e517d97ae562ca933ec0d9942b617a

Aliases

arxiv: 1811.07181 · arxiv_version: 1811.07181v1 · doi: 10.48550/arxiv.1811.07181 · pith_short_12: HL3NJBEFQD6O · pith_short_16: HL3NJBEFQD6OFUCI · pith_short_8: HL3NJBEF

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/HL3NJBEFQD6OFUCINT44MMBJGT \
  | 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: 3af6d4848580fce2d0486cf9c6302934d8e517d97ae562ca933ec0d9942b617a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5d9a871e9486c8b369c1092acde5f9f1b7170d79b3957d0c5d35f58d7be1e70",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-11-17T15:33:32Z",
    "title_canon_sha256": "032b0923ba7456b34daa16646d4f89018cb6a1c4ecf488cee897e3976b1b65a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.07181",
    "kind": "arxiv",
    "version": 1
  }
}