Pith Number

pith:WBK3HIRO

pith:2013:WBK3HIRORDJ2KXB2ISLX2S6Z3X

not attested not anchored not stored refs pending

Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel

Jianglong Wu, Qingguo Liu

arxiv:1304.4434 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{WBK3HIRORDJ2KXB2ISLX2S6Z3X}

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	2026-05-18T02:54:47.078810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b055b3a22e88d3a55c3a44977d4bd9ddcd130f834b096121fdfd0b4ece1d9f41

Aliases

arxiv: 1304.4434 · arxiv_version: 1304.4434v1 · doi: 10.48550/arxiv.1304.4434 · pith_short_12: WBK3HIRORDJ2 · pith_short_16: WBK3HIRORDJ2KXB2 · pith_short_8: WBK3HIRO

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/WBK3HIRORDJ2KXB2ISLX2S6Z3X \
  | 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: b055b3a22e88d3a55c3a44977d4bd9ddcd130f834b096121fdfd0b4ece1d9f41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4006d06262ae1f1b273c69b83fac87b4710b0747a861ec1178017310f87e187d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-04-16T13:28:32Z",
    "title_canon_sha256": "0151dc3aba2eb613ceec4be52a5eb1a13c553e4c8f3a0b090625eac88fc8ef39"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.4434",
    "kind": "arxiv",
    "version": 1
  }
}