Pith Number

pith:RLEGRIR4

pith:2015:RLEGRIR42XQP7Z47LWKL5ZV7VF

not attested not anchored not stored refs pending

Sharp reversed Hardy-Littlewood-Sobolev inequality on $\mathbb R^n$

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

arxiv:1508.02041 v2 · 2015-08-09 · 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{RLEGRIR42XQP7Z47LWKL5ZV7VF}

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	2026-05-18T00:06:51.685407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ac868a23cd5e0ffe79f5d94bee6bfa965ddb98f07d3e4edd41409469070ae07

Aliases

arxiv: 1508.02041 · arxiv_version: 1508.02041v2 · doi: 10.48550/arxiv.1508.02041 · pith_short_12: RLEGRIR42XQP · pith_short_16: RLEGRIR42XQP7Z47 · pith_short_8: RLEGRIR4

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/RLEGRIR42XQP7Z47LWKL5ZV7VF \
  | 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: 8ac868a23cd5e0ffe79f5d94bee6bfa965ddb98f07d3e4edd41409469070ae07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9e5fa47bf25de16402fb62d47b9a00387ad08c898f6a0da4233dc8ec133b33c",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-08-09T15:40:07Z",
    "title_canon_sha256": "a9f7ff27dcffc929fc62a0c646e267d2c2190b6c9c69a1bc0db43f0b638489fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02041",
    "kind": "arxiv",
    "version": 2
  }
}