Pith Number

pith:YBO4C7XN

pith:2008:YBO4C7XNVTR5WCQR4HKA5Q3XLK

not attested not anchored not stored refs pending

$L^p$ Boundedness of Commutators of Riesz Transforms associated to Schr\"{o}dinger Operator

Lizhong Peng, Pengtao Li, Zihua Guo

arxiv:0802.3128 v1 · 2008-02-21 · 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{YBO4C7XNVTR5WCQR4HKA5Q3XLK}

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	2026-05-18T02:16:00.952491Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c05dc17eedace3db0a11e1d40ec3775ab20ef08e8b45dbc724338ef2c0b87a57

Aliases

arxiv: 0802.3128 · arxiv_version: 0802.3128v1 · doi: 10.48550/arxiv.0802.3128 · pith_short_12: YBO4C7XNVTR5 · pith_short_16: YBO4C7XNVTR5WCQR · pith_short_8: YBO4C7XN

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/YBO4C7XNVTR5WCQR4HKA5Q3XLK \
  | 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: c05dc17eedace3db0a11e1d40ec3775ab20ef08e8b45dbc724338ef2c0b87a57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3d40b5c3834bd269b20f5d7ddfa740cfb676ffd04d05b2005ab39e6e14b0757",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2008-02-21T15:10:44Z",
    "title_canon_sha256": "f531a598caa691b3e31c8ecad4d0182397ad704efdc6b8393eceaa4f7b3b617a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0802.3128",
    "kind": "arxiv",
    "version": 1
  }
}