Pith Number

pith:FTWCKOTI

pith:2011:FTWCKOTIWXECTP542VN5ZGXP2J

not attested not anchored not stored refs pending

Boundedness of oscillatory integral operators and their commutators on weighted Morrey spaces

Shanzhen Lu, Shaoguang Shi, Zunwei Fu

arxiv:1111.5109 v1 · 2011-11-22 · 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{FTWCKOTIWXECTP542VN5ZGXP2J}

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	2026-05-18T04:07:53.423685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2cec253a68b5c829bfbcd55bdc9aefd2514aefa34deaa81712478ee9d83e36c0

Aliases

arxiv: 1111.5109 · arxiv_version: 1111.5109v1 · doi: 10.48550/arxiv.1111.5109 · pith_short_12: FTWCKOTIWXEC · pith_short_16: FTWCKOTIWXECTP54 · pith_short_8: FTWCKOTI

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/FTWCKOTIWXECTP542VN5ZGXP2J \
  | 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: 2cec253a68b5c829bfbcd55bdc9aefd2514aefa34deaa81712478ee9d83e36c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86a6ad78d6a586d12943018933af550e31e79f4209c51b6e77331dcc446e7962",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-11-22T06:10:27Z",
    "title_canon_sha256": "0ca65b4fb25471da68aa23f6471b5c702bac65936b2461de6caf7a4bad50a03a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5109",
    "kind": "arxiv",
    "version": 1
  }
}