Pith Number

pith:MV7IYSQL

pith:2015:MV7IYSQLMXKPDVMMUBDUBIWVLJ

not attested not anchored not stored refs pending

Sharp reversed Hardy--Littlewood--Sobolev inequality on the half space $\mathbb R_+^n$

Qu\^oc-Anh Ng\^o, Van Hoang Nguyen

arxiv:1510.04680 v2 · 2015-10-15 · math.AP · 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{MV7IYSQLMXKPDVMMUBDUBIWVLJ}

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	2026-05-18T00:06:51.676629Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

657e8c4a0b65d4f1d58ca04740a2d55a42248b5c952fb3290313df1c01a71310

Aliases

arxiv: 1510.04680 · arxiv_version: 1510.04680v2 · doi: 10.48550/arxiv.1510.04680 · pith_short_12: MV7IYSQLMXKP · pith_short_16: MV7IYSQLMXKPDVMM · pith_short_8: MV7IYSQL

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/MV7IYSQLMXKPDVMMUBDUBIWVLJ \
  | 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: 657e8c4a0b65d4f1d58ca04740a2d55a42248b5c952fb3290313df1c01a71310

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "312581171f2053a8dd008bdceca5efcb34eda918430e9688ab8ed51d9d2b9334",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-10-15T19:39:31Z",
    "title_canon_sha256": "d8054dfdbffe91f7a559edc24cda5557431f1a9b4b488df88e5ace2f395f84e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.04680",
    "kind": "arxiv",
    "version": 2
  }
}