Pith Number

pith:7ZTKTQWL

pith:2024:7ZTKTQWLPAF2CYHYL4HCKOXCFG

not attested not anchored not stored refs pending

Real-variable Theory of Anisotropic Musielak-Orlicz-Lorentz Hardy Spaces with Applications to Calder\'{o}n-Zygmund Operators

Wenhua Wang, Xiong Liu

arxiv:2410.06611 v2 · 2024-10-09 · math.CA · 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{7ZTKTQWLPAF2CYHYL4HCKOXCFG}

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	2026-07-05T11:09:01.318297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe66a9c2cb780ba160f85f0e253ae2299d2535846a506be4ba10f4c4315b4f9a

Aliases

arxiv: 2410.06611 · arxiv_version: 2410.06611v2 · doi: 10.48550/arxiv.2410.06611 · pith_short_12: 7ZTKTQWLPAF2 · pith_short_16: 7ZTKTQWLPAF2CYHY · pith_short_8: 7ZTKTQWL

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/7ZTKTQWLPAF2CYHYL4HCKOXCFG \
  | 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: fe66a9c2cb780ba160f85f0e253ae2299d2535846a506be4ba10f4c4315b4f9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "047a8132b2494ede72e50f0b8cd73bdc42d5d54e7a6ae073d5c840e834f2fe1e",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2024-10-09T07:05:08Z",
    "title_canon_sha256": "9d46563ac490aef61e30ad5711dd72695bf1a813c6a43d6e2d9001f6d7b5fea1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.06611",
    "kind": "arxiv",
    "version": 2
  }
}