Pith Number

pith:CL3SINHH

pith:2023:CL3SINHHIBSLSLGEF6W6WTF66Q

not attested not anchored not stored refs pending

Commutators of the maximal and sharp functions with weighted Lipschitz functions

Pu Zhang, Xiaomeng Zhu

arxiv:2307.15500 v2 · 2023-07-28 · math.CA · math.AP · 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{CL3SINHHIBSLSLGEF6W6WTF66Q}

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	2026-07-05T07:33:18.385187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12f72434e74064b92cc42fadeb4cbef41d485adce2760d4ff2442a7852f1946a

Aliases

arxiv: 2307.15500 · arxiv_version: 2307.15500v2 · doi: 10.48550/arxiv.2307.15500 · pith_short_12: CL3SINHHIBSL · pith_short_16: CL3SINHHIBSLSLGE · pith_short_8: CL3SINHH

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/CL3SINHHIBSLSLGEF6W6WTF66Q \
  | 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: 12f72434e74064b92cc42fadeb4cbef41d485adce2760d4ff2442a7852f1946a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5165e9649dfdbf33fa90eccb6d785ddce2760c17f1c67f03b33cffe37f93981b",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2023-07-28T11:52:41Z",
    "title_canon_sha256": "a033091aa3c1d2c430d404c9e9f8d8e4072c45b9133ab75bfec4ad6e5e0b1e4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.15500",
    "kind": "arxiv",
    "version": 2
  }
}