Pith Number

pith:G4LXEXH5

pith:2018:G4LXEXH5EGVUAN754I75BOTOYG

not attested not anchored not stored refs pending

Some estimates for the bilinear fractional integrals on the Morrey space

Huihui Zhang, Jianmiao Ruan, Xiangxing Tao, Xiao Yu

arxiv:1808.05189 v1 · 2018-08-15 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G4LXEXH5EGVUAN754I75BOTOYG}

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	2026-05-18T00:08:01.369689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3717725cfd21ab4037fde23fd0ba6ec180d9a9bb80ab057874a3ec6c2925d108

Aliases

arxiv: 1808.05189 · arxiv_version: 1808.05189v1 · doi: 10.48550/arxiv.1808.05189 · pith_short_12: G4LXEXH5EGVU · pith_short_16: G4LXEXH5EGVUAN75 · pith_short_8: G4LXEXH5

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/G4LXEXH5EGVUAN754I75BOTOYG \
  | 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: 3717725cfd21ab4037fde23fd0ba6ec180d9a9bb80ab057874a3ec6c2925d108

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7a28f68321077b38419c0470f01175a76b75ec903d6dcfb4dabca442a7919f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-08-15T17:17:31Z",
    "title_canon_sha256": "e4245f5df7b9154259ed206fdc63bb4ea3dc8bb167b8beeae88c42117873746b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.05189",
    "kind": "arxiv",
    "version": 1
  }
}