Pith Number

pith:7ZT6Q52S

pith:2012:7ZT6Q52SJ3H7VFAQXYNHB5BZTC

not attested not anchored not stored refs pending

Weighted Lipschitz estiamtes for commutators of one-sided operators on one-sided Triebel-Lizorkin spaces

Guang Lan Wang, Qing Yan Wu, Zun Wei Fu

arxiv:1206.0383 v1 · 2012-06-02 · 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{7ZT6Q52SJ3H7VFAQXYNHB5BZTC}

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	2026-05-18T03:54:17.810873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe67e877524ecffa9410be1a70f43998867226cc1f188dd5635fe6b61cf9ec20

Aliases

arxiv: 1206.0383 · arxiv_version: 1206.0383v1 · doi: 10.48550/arxiv.1206.0383 · pith_short_12: 7ZT6Q52SJ3H7 · pith_short_16: 7ZT6Q52SJ3H7VFAQ · pith_short_8: 7ZT6Q52S

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/7ZT6Q52SJ3H7VFAQXYNHB5BZTC \
  | 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: fe67e877524ecffa9410be1a70f43998867226cc1f188dd5635fe6b61cf9ec20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78a6132f4b8a4cccb4239f3ca168dd5c4cb933fc8e0b8e72aee6715b5f90d140",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-06-02T13:44:44Z",
    "title_canon_sha256": "2b2d84d69a7c05d136a06f611850da3b7764fefe6fc140209ff5f39dff2b69e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0383",
    "kind": "arxiv",
    "version": 1
  }
}