Pith Number

pith:4NPT32UY

pith:2023:4NPT32UYRN5L4NTK6ZBO4BAYTO

not attested not anchored not stored refs pending

Weak type $(1, 1)$ of Riesz transform on some direct product manifolds with exponential volume growth

Hong-Quan Li, Jie-Xiang Zhu

arxiv:2304.04335 v1 · 2023-04-10 · 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{4NPT32UYRN5L4NTK6ZBO4BAYTO}

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.

Cited by

1 paper in Pith

Hardy-Littlewood maximal operator on spaces of exponential volume growth

Receipt and verification

First computed	2026-07-05T05:59:25.116683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e35f3dea988b7abe366af642ee04189bbb5affcdfec83a511782ff6daa91074e

Aliases

arxiv: 2304.04335 · arxiv_version: 2304.04335v1 · doi: 10.48550/arxiv.2304.04335 · pith_short_12: 4NPT32UYRN5L · pith_short_16: 4NPT32UYRN5L4NTK · pith_short_8: 4NPT32UY

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/4NPT32UYRN5L4NTK6ZBO4BAYTO \
  | 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: e35f3dea988b7abe366af642ee04189bbb5affcdfec83a511782ff6daa91074e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3e8e394fe3bab07275220cd34d1f04dc4bbe465ecade0adfc6205a39f614df8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2023-04-10T00:24:36Z",
    "title_canon_sha256": "8a6a6eac291025761f98c19a6ab5a52cd7038b0703a68059d930f02718d73369"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2304.04335",
    "kind": "arxiv",
    "version": 1
  }
}