Pith Number

pith:JJWDVNSP

pith:2022:JJWDVNSPTJ3YWD6RR2U3SR3TOT

not attested not anchored not stored refs pending

The Characterizations of Anisotropic Mixed-Norm Hardy Spaces on $\mathbb{R}^n$ by Atoms and Molecules

Aiting Wang, Wenhua Wang

arxiv:2203.07611 v1 · 2022-03-15 · math.FA · 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{JJWDVNSPTJ3YWD6RR2U3SR3TOT}

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	2026-07-05T04:05:20.532521Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a6c3ab64f9a778b0fd18ea9b9477374ed31fe8e16a419adc6bede34d31a7248

Aliases

arxiv: 2203.07611 · arxiv_version: 2203.07611v1 · doi: 10.48550/arxiv.2203.07611 · pith_short_12: JJWDVNSPTJ3Y · pith_short_16: JJWDVNSPTJ3YWD6R · pith_short_8: JJWDVNSP

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/JJWDVNSPTJ3YWD6RR2U3SR3TOT \
  | 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: 4a6c3ab64f9a778b0fd18ea9b9477374ed31fe8e16a419adc6bede34d31a7248

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d914369cd8ccffbf032ecd9bd7a967c387c28fbdfaa7c770b8a08f0afe75197",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2022-03-15T02:58:57Z",
    "title_canon_sha256": "b9575748f7ada3eba7deef5984088253cdee41926fae19d942385a2a1ae86727"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.07611",
    "kind": "arxiv",
    "version": 1
  }
}