Pith Number

pith:YZLX4P4D

pith:2013:YZLX4P4DA4ACGNCWRQMISVQ3NB

not attested not anchored not stored refs pending

Weighted Endpoint Estimates for Multilinear Commutators of Marcinkiewicz Integrals

Jianglong Wu, Qingguo Liu

arxiv:1304.4431 v1 · 2013-04-16 · 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{YZLX4P4DA4ACGNCWRQMISVQ3NB}

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	2026-05-18T03:27:53.113856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6577e3f8307002334568c1889561b684637a4515e06bb7223cf0eb5d4971837

Aliases

arxiv: 1304.4431 · arxiv_version: 1304.4431v1 · doi: 10.48550/arxiv.1304.4431 · pith_short_12: YZLX4P4DA4AC · pith_short_16: YZLX4P4DA4ACGNCW · pith_short_8: YZLX4P4D

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/YZLX4P4DA4ACGNCWRQMISVQ3NB \
  | 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: c6577e3f8307002334568c1889561b684637a4515e06bb7223cf0eb5d4971837

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2cb2cba41af9f8c4a0a5aaac3fcc4021a6e2677c17cb16e9a4dca854fb1a4001",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-04-16T13:15:43Z",
    "title_canon_sha256": "48d4acc06601002bf5922338e4e1aac8481c125c7bdaa70ed163f99f1dc0e02b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.4431",
    "kind": "arxiv",
    "version": 1
  }
}