Pith Number

pith:EX7E32QZ

pith:2018:EX7E32QZEHAAUGJSGCAVWRBFGD

not attested not anchored not stored refs pending

Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups

Aidyn Kassymov, Durvudkhan Suragan, Michael Ruzhansky

arxiv:1810.11439 v1 · 2018-10-26 · 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{EX7E32QZEHAAUGJSGCAVWRBFGD}

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	2026-05-18T00:02:14.174251Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

25fe4dea1921c00a193230815b442530ee89e55635b21131fdf1427da031c018

Aliases

arxiv: 1810.11439 · arxiv_version: 1810.11439v1 · doi: 10.48550/arxiv.1810.11439 · pith_short_12: EX7E32QZEHAA · pith_short_16: EX7E32QZEHAAUGJS · pith_short_8: EX7E32QZ

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/EX7E32QZEHAAUGJSGCAVWRBFGD \
  | 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: 25fe4dea1921c00a193230815b442530ee89e55635b21131fdf1427da031c018

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d7d61505d7d6dee51d35216032fdff5bae61f6c414bae3cef58d1817eca2894",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-10-26T17:43:50Z",
    "title_canon_sha256": "68bc00538c1e19adaec02abdfa974d681ab1f9d4338f2532841e8d0e985d6de1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.11439",
    "kind": "arxiv",
    "version": 1
  }
}