Pith Number

pith:JKFOB7GZ

pith:2012:JKFOB7GZL24GOFFIVD4ZFEQQUS

not attested not anchored not stored refs pending

Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces

Zengyan Si

arxiv:1203.4407 v2 · 2012-03-20 · 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{JKFOB7GZL24GOFFIVD4ZFEQQUS}

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	2026-05-18T03:59:28.760399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a8ae0fcd95eb86714a8a8f9929210a4aff057c721f3f57e4d62721a9fe33ccd

Aliases

arxiv: 1203.4407 · arxiv_version: 1203.4407v2 · doi: 10.48550/arxiv.1203.4407 · pith_short_12: JKFOB7GZL24G · pith_short_16: JKFOB7GZL24GOFFI · pith_short_8: JKFOB7GZ

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/JKFOB7GZL24GOFFIVD4ZFEQQUS \
  | 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: 4a8ae0fcd95eb86714a8a8f9929210a4aff057c721f3f57e4d62721a9fe33ccd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc95a8f879332fdf629e1dcc141864ad8d87a5fc9b9d8e6a5ce46a66644f1d31",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-03-20T12:24:18Z",
    "title_canon_sha256": "9e7ab172ffac200ebf5773daee34a078cabec490fdc8413ccbd86d02aee74dfa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4407",
    "kind": "arxiv",
    "version": 2
  }
}