Pith Number

pith:XGQDSKIN

pith:2016:XGQDSKIN7YMTNUZE5GFD542DFI

not attested not anchored not stored refs pending

Subcritical Approach to Sharp Hardy-Littlewood-Sobolev Type Inequalities on the Upper Half Space

Jingbo Dou, Meijun Zhu, Qianqiao Guo

arxiv:1610.05835 v2 · 2016-10-19 · 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{XGQDSKIN7YMTNUZE5GFD542DFI}

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	2026-05-18T00:49:06.470695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9a039290dfe1936d324e98a3ef3432a3dbf850bb4d5b28dd6198b6cf28e9388

Aliases

arxiv: 1610.05835 · arxiv_version: 1610.05835v2 · doi: 10.48550/arxiv.1610.05835 · pith_short_12: XGQDSKIN7YMT · pith_short_16: XGQDSKIN7YMTNUZE · pith_short_8: XGQDSKIN

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/XGQDSKIN7YMTNUZE5GFD542DFI \
  | 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: b9a039290dfe1936d324e98a3ef3432a3dbf850bb4d5b28dd6198b6cf28e9388

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dff1b7b0845ac8879a7246e281e85c2bb8ea3fbf6c5485b99d96d17d444a0cb0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-10-19T01:11:37Z",
    "title_canon_sha256": "2f44efe4e6967ea92a08048670f36980d58c6d0cfced4ac48ecf8edd4ad5673b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.05835",
    "kind": "arxiv",
    "version": 2
  }
}