Pith Number

pith:FL7W73U7

pith:2021:FL7W73U75N3HGLL76VSVG2YD4O

not attested not anchored not stored refs pending

The Boundedness of Fractional Integral Operators in Local and Global Mixed Morrey-type Spaces

Houkun Zhang, Jiang Zhou

arxiv:2102.01304 v2 · 2021-02-02 · 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{FL7W73U75N3HGLL76VSVG2YD4O}

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	2026-07-05T03:05:00.865464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2aff6fee9feb76732d7ff565536b03e3bb1c3ccf1ae4dd40606dbfbce5ee5849

Aliases

arxiv: 2102.01304 · arxiv_version: 2102.01304v2 · doi: 10.48550/arxiv.2102.01304 · pith_short_12: FL7W73U75N3H · pith_short_16: FL7W73U75N3HGLL7 · pith_short_8: FL7W73U7

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/FL7W73U75N3HGLL76VSVG2YD4O \
  | 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: 2aff6fee9feb76732d7ff565536b03e3bb1c3ccf1ae4dd40606dbfbce5ee5849

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2df5d70482f80f9eafae672672839e445b8a732a3755311e6f92bd49fa4f792c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2021-02-02T04:25:43Z",
    "title_canon_sha256": "2c9b317b62327d920143d5702e4ad7dbc3e2529c27c8f04a671c7bbf4ed98247"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.01304",
    "kind": "arxiv",
    "version": 2
  }
}